Considering it is a continuation of an existing franchise, it won't be possible for me to evaluate it based on its own.
I will use Japanese Terms mainly because I watched it mainly in Japanese. Whenver I know the English Terms, I will use them.

Story
Dragon Ball GT is a sequel to the original Anime Adaptation of Toriyama's Dragon Ball manga and thus the third series following Dragon Ball and Dragon Ball Z.
An old enemy of the Main Character Son Goku discovered the existence of another set of Dragon Balls in the Heavenly Realm also called the Lookout.
These Dragon Balls have been sealed away for reasons not even the eldery Prince Pilaf knows. By accident he wishes from the new Dragon Balls Son Goku back into a kid.
These new sets of Dragon Balls created by the Former God before he split into Kami and Piccolo have the downside that they destroy the planet they were last used. And to stop that, they need to be brought back in time to their resting place before that happens to prevent said destruction.
Thus Goku, Trunks and Goku's granddaughter Pan have to travel through space to collect the now scattered Ultimate Dragon Balls aka. Black Star Dragon Balls.

Dragon Ball GT decided to make the Dragon Balls the focus on the story and they did several things to fix this problem. First is giving them consequences. While these consequences aren't big, it is a reasonable reason to start the adventure.
Another thing is obviously the Dragon Balls splitting to space. Space is vast and not much of it was explored in Dragon Ball, including in Dragon Ball Z filler.
Lastly is turning Goku into a kid. Goku as that point was a completely different tier of fighter. He is the strongest fighter in the Universe and can teleport anywhere under the right circumstances. To fix that issue, Goku was nerfed with an immature body restricting him to use the most powerful techniques and the ability to control his full power. As in one episode Goku accidently blew up a volcano instead of stopping the eruption.
It also made him fit better to comic relief scenes. But his character itself wasn't affected by his new body.

But trying to do such a story comes at a price. Fans of Dragon Ball have become used to the action and high stake fights in DBZ. Thus an adventure series, regardless how wholesome it is, felt boring.
GT had a good atmosphere the early episodes, but a lot of questionable things happened around episode 6 or so. The transition to the high stake fights fans were looking for wasn't done that well and the fight against God of Destruction Luud raised a few eyebrows regarding the crews strength.
However, the ending of this arc and pretty much ever GT arc is very satisfying. There is at least 1 or 2 very engaging battles such as against General Rildo and the first major antagonist following to the next arc, Baby.

GT would eventually switch from DB adventure mode to DBZ's punching a badguy invading earth very hard. Many would consider GT to be a series with Good Idea and Bad Execution. The Baby Saga doesn't just have good ideas, but has also good execution.
It has some parallels to the Saiyan and Frieza Saga focusing on Saiyan's history. But unlike the Saiyans being the enemy, they are the ones surpressed. Unlike in the Frieza arc where the enemy is just an aggressor of the Saiyans, it is a victim who wants justice.
It is a very engaging story with very high stakes. Goku's best move is almost sealed in the Genkidama aka Spirit Bomb. Most allies are enemies. The Dragon Balls aren't as accessable to immediately solve everything. And Goku can't use his Teleportation to ask help from specific allies.

The next arc is mostly considered the worst arc since its idea doesn't appear to be original. In hell, the scientist Dr Mu meets with Dr Gero. They team up to create a new enemy with their combined technology: Hell Fighter 17. An enemy that looks like Android 17. In the Japanese version it was stated that Android 17 has hidden powers that apparently surpasses Cell's and they want to brainwash and awaken him with his new technology. That leads to the Gate of Hell opening in the living world where old foes terrorize earth.
The goal is to stop the scientist, the old nemesis and both 17 who merged to Super 17.
The arc is insanely short. While many characters are involved and are useful, we don't see much to get a lot of this arc. Most of it is wasted on comic relief with Goku.
The final fight is a double edged sword with a strong beginning, a mediocre middle part and ok ending.

The last arc is one with the most potential. The Dragon Balls got cracked and all the negative energy was released creating the Shadow Dragons. Their power is independent from Dende and their power wary based on how much negative energy was generated from the wish.
GT gave all Dragon Balls a negative consequence and thus this arc raises the stakes to a level not seen before. Now all problems can't be solved with just wishing them away since each wish could generate more negative energy and more Shadow Dragons in the future.
Sadly the arc has a weak beginning. The first Shadow Dragons were defeated by plot convinience. Most allies sat back while Pan, Goku and Giru did most the work.
The only ones excused are Bulma and Vegeta.
Emotional conflict and good action would eventually happen once the 7-Star Dragon appeared. There were still some questionable fights inbetween, but overall the last 3 Shadow Dragon fights are considered the highlight of the final arc.
GT's ending is bombastic and many consider it a satisfying conclusion to Dragon Ball. Including fans that don't like GT.
Baby arc is without a doubt the reason to watch GT. The Shadow Dragon arc has a good concept with bad execution, but its highs are very high.
The other arcs are mediocre but both end either satisfying or aren't too long to cause much damage.

Characters
Pan has been shown to be a very unreliable member. She only exist to be a damsel in distress but eventually saving her helped the crew to find another piece of a puzzle. Pan has been shown to be a good aid when it came to defeat Luud and also came in clutch in many other fights. However, not for the reasons fans would hope. And she never reached the potential anyone hoped her to do like her father Gohan in Dragon Ball Z.
Pan starts off looking down on her grandpa Goku who became a child. Over the course of the series she would eventually respect him and help him to overcome some of the most difficult challenges.
Besides the 17 arc, she has been very prominent in all of GT so far. I heard she is annoying in English, but in the Japanese version I felt her far more tolerable.

Trunks is not very prominent besides the first arc. Unlike his future counterpart, he is taking more a mechanical role in GT and the member who keeps the group together. For people expecting him to get amazing fights, Trunks won't be satisfying. But he is coming very clutch when it was about to stop Dr. Mu in the Ultimate Dragon arc.
He also showed courage in the face of an enemy like Yixinglong aka. Omega Shenron trying to buy time for Goku and Vegeta to perform fusion.

Giru is a Machine Mutant who merged with the Dragon Radar. He was very suspicious but eventually became a core member of the crew. Solving certain issues and helping Pan out. He also helped Trunks' plan by acting as a double agent to expose Dr. Mu.

Son Goku is not very active character wise in the first arc. He is more like the wise mentor type of figure in the group. Able to analyse and adapt to fights as he was portrayed in Z. But most of it is seen best in the fight against Rildo and after.
Goku went through several character arcs where he overcame challenges and misconceptions people have about Goku in Z. He overcame the Golden Oozaru. A powered up version of his giant monkey form in which he killed his grandpa in as a child. He learned to embrace and accept his Saiyan heritage fully and killed the last Tsufuru (or Tuffle). Mainly because Baby dared to lay his hands on his family.
Goku would also take responsibility at the end for the Dragon Balls and honestly for a lot of things.
If anything, with GT Goku's character went full circle ending his story in a very satisfying way.

Vegeta despite not being a main character had a lot of prominence. He overcame his obsession with Goku since the Boo Saga and adapted to his earthly lifestyle. As a character he is very enjoyable to watch.
Sadly Vegeta has no major victories as per usual. But also has not a lot of prominent fights.
In the English version they took all that away with makes it awkward to watch.

Baby is probably one of the best antagonists in the franchise. After losing his home planet to the Saiyans, he created Dr. Mu to collect him energy for several decades. Baby's goal is to create a new Tsufuru race and take revenge on the ones that wronged them. Sadly that have to be also the now peaceful descendants of the Saiyans.
Baby contrary to his people is portrayed as pure evil. But to rebuild his race and being part of a royal bloodline, it can be argued that he feels its justified. Baby stopped seriously harming people after his evolution completed and he took over Vegeta's body (as he is a parasitic lifeform).
We see how the new Tsufurus look up to Baby, how he greets them and appreciates them. But when he sees a Saiyan like Goku, his trauma kicks in where he would become the devil and even use his own underlings as a shield.
Baby is the kind of villain that learns from his mistakes. Each confrontation he lost, he got something different and tried a new strategy to get what he wanted. Eventually he succeeded.
Seeing that Goku has things he cares about, he is willing to use them to get the upper hand. For example a scene I liked is when Baby turned his back on Goku and fired an attack on earth. Purposely failing so Goku would stand before him to take the next attack full on.
There are several scenes like that that keep the fight engaging.

Super 17 started off as a generic underling character. He is a fusion of Hell Fighter 17 and the fully awakened Android 17. His design and fighting style is almost elegant. Even if the fight isn't very entertaining, it is beautiful to see him react. Even during the least enjoyable portion of his fight against Goku, he was vibing. He screams "I am too cool to lose to you.".
My favorite moment is his interaction with Android 18. 18 so far didn't do anything in GT. She lost her husband again and was beaten up by her brainwashed brother. She tried to reach his heart once more her own way which allowed 17 to regain his freedom from Dr Mu's control and try to do his own thing. It was a very satisfying moment for an antagonist with "no" character.

Shadow Dragons are a mixed back. Yixinglong is the leader and has a similar presents to Frieza. He is willing to kill his own kind if it is to get what he wants. But he is also prideful giving his opponents a chance to fight him as long as he knows they can't win.
Suxinglong aka. Nova Shenron is the most selfless dragon born from the most selfish wish. He represents the 4-Star ball and is the most honorable member of the dragons. Prefering a fair fight and sparing children and woman. He is one of the characters who gained Goku's respect. His brother Sanxinglong aka. Eis Shenron is the polar opposite. He as the 3-Star dragon and like the 7-Star Dragon use others as a shield and tries to win by any means.

Other characters have minimal roles. It would be a waste to talk about each. There are some really good arcs inbetween some, but I think I mentioned the most important ones with as little spoilers as possible.

I am not much into using music to evaluate shows. The opening of Japanese GT is probably one of the best with Chala Head Chala. Music is placed in the most appropriate scenes. I personally like the use of silence in some scenes to create tension before a fight or after. One just has to watch Goku vs. Ledgic to get what I mean.
The Shadow Dragon OST feels like beings from a different realm appeared or mystery. It is not clear what they truly want and what dangers awaits us.

It is very enjoyable if one doesn't simply watch for the battles. The battles are short and bite sized. It has some really good jokes. And while there isn't much slice of life, when those scenes appear especially with Vegeta, they are enjoyable to watch.

Art... I don't really care much about it. But GT may be the best looking Dragon Ball series so far. Very few episodes look awful and animation is pretty fluid.

With this I end my review of Dragon Ball GT. Like Toriyama-Sensei would say, it’ll make me happy for us to watch and enjoy it together.