Otakus are the pride of Japanese culture!" After watching Lucky Star in its entirety, you want to take this sentence seriously. Lucky Star is a real otaku anime, but unlike Genshiken, it doesn't focus on any otaku relationships, but pure slice-of-life and tons of comedy and parody. In principle, the complete frame story of Lucky Star can be summed up in one word: Everyday life. No superheroes with superhuman powers that no one is supposed to know about? No ten-meter fighting robots? No Transformer-like space battles? No horror, ecchi or hentai? Just four girls in high school like you and me? Is that even possible? Since Azumanga Daioh or Gakuen Utopia Manabi Straight! we know: Very well!

The most important characters are Konata, Kagami, Tsukasa and Miyuki.
Konata is intelligent and very athletic. Unfortunately she is incredibly lazy, an otaku and she spends most of the day playing MMORPGs and adult games.
Kagami is the older twin sister of Tsukasa and a "tsundere" as they come. She goes to the same class as the others and she and Konata always clash, but are good friends.
Tsukasa is the younger twin sister. She is good-natured and can cook well, but doesn't have much in her head and often only understands train stations.
Miyuki wears glasses, is very rich and polite. However, she is a klutz and is afraid of the dentist, yet she has to go there for treatment surprisingly often.

She is joined by Konata's father, Konata's cousin Yui and her little sister Yutaka, as well as Yutaka's new classmates and two of Kagami's class.

Animation:
Yes, the most important thing to me for my first impression is always the animation and design of the characters. From Kyoto Animation we already know eye candy like Full Metal Panic! The Second Raid, Air or The Melancholy of Haruhi Suzumiya and although it doesn't look like it at first glance, KyoAni seems to have put a lot of effort into it again this time. Watch the cheerleader dance in the opening - there are professionals at work here! The characters are "moe" style, meaning extremely cutely drawn and look far younger than they actually are.
The overall look, however, doesn't convey a 2007 anime: a fellow anime fan from my acquaintance wouldn't believe me at first that Lucky Star was a 2007 production. However, the gaudy color scheme and the low-detail but very picturesque backgrounds and the colorless extras round out the atmosphere of Lucky Star perfectly.
I think all the features that were criticized, like the uninteresting backgrounds or the colorless (and sometimes only implied) extras, which even only 2 voice actors have to share, are absolutely intentional.
You are supposed to concentrate completely on the characters, which actually works. But sometimes you concentrate so hard that you miss all the eye-catchers.
And that's what impressed me about Lucky Star: Every episode has certain eye-catchers, like an Ed Cosplayer from Fullmetal Alchemist or the posters in Konata's room. Lucky Star has a high rewatch factor, only on the second viewing (sometimes even on the third) I noticed things that almost made me laugh to death, but which I overlooked the first time. (watch episode 1 at ~0:15:45, when Kagami comes into the classroom, the two guys on the left in the picture).
But you should have seen a few anime before to understand the hints and eye-catchers. These include: Fate/stay night, Full Metal Panic, The Melancholy of Haruhi Suzumiya, Shuffle! and you better also know how the races in Initial D go :)
By the way, Lucky Star is the ONLY anime I know that takes place in our world. Every place our 4 heroines visit, be it the Animate store in Saitama, the FamilyMart where Kagami buys a drink ,the famous fast food restaurant with the golden M, the Comiket or even the building of KyotoAnimation itself, everything was researched in detail and transferred almost perfectly 1:1. The temple (seen in the opening) where the Hiiragi sisters work in Lucky Star experienced a veritable otaki onslaught after Newtype printed directions to the plot locations

Story:
There is no story. No super-villain who wants to take over the world? No.
The only thing that drives the story is time. Thus, Lucky Star begins with Konata & Co shortly after entering the 2nd grade of high school and ends, like Azumanga Daioh, shortly before the end of the 3rd grade.
There's not much to say about the content because of that. Lucky Star is also a yonkoma manga, so instead of one long storyline, there are several short ones, and there is no common thread running through the series, which is what makes Lucky Star unique. If I didn't have the time bar at the bottom of the screen, I wouldn't be able to tell when the episode is over. When it's over, there's the Lucky Channel, which was originally supposed to be an information show about the series, hosted by young idol Akira Kogami and Minoru Shiraishi. Minoru Shiraishi is Konata's normal classmate in Lucky Star, but in reality is a voice actor (e.g. Taniguchi in The Melancholy of Haruhi Suzumiya) who virtually plays himself this time.
Akira's peculiar personality (must see!) and Minoru's talent for making Akira freak out over and over again make the show fail miserably almost every time.

Sound, Music, OP and ED.
With a few exceptions, the entire repertoire of background music is taken from other anime (the Eurobeat during the relay race is from Initial D, for example).
Only the opening is really from Lucky Star and as already said here it's colorful, squeaky and totally crazy, just like Lucky Star is.
Endings are for every episode. While we only see the door of the karaoke room until episode 12 and listen to the karaoke of our 4 friends to different anime songs (including Cha-La-Head-Cha-La from Dragonball Z or the opening of Full Metal Panic? Fumoffu), Minoru Shiraishi himself (in live-action) delights us with his performance of various anime songs from episode 13 upwards.

Conclusion and all:
Lucky Star is not a masterpiece but still cult. The first episode in which only about grilled steaks, puddings and chocolate croissants is babbled is the perfect introduction. You think to yourself: either you're such a hardcore anime freak and go through with it now - or you turn off yawning and never watch it again. The ones who made it are happy now, because Lucky Star gets funnier with every episode when the other classmates join in and it gets even better! Maybe the first episode is supposed to separate the wheat from the chaff, maybe that was unintentional, but a whole episode about topics that I don't even need 5 minutes for... not bad.
Comedy and slice-of-life fans, hardcore freaks, and people who need a break between the more challenging anime should, or even must(!), tune in.
If you haven't seen Lucky Star yet, you definitely missed something.
Deductions were made for the high level of "anime knowledge" you need, but if you don't have that, you should leave this one alone and watch the anime suggested above first.

Lucky Star gets 93% from me.