Watching Lucky Star without watching Haruhi first is like watching Space Balls without watching Star Wars first.
Based on Clannad and Angel Beats, I think you would like Ano Hana, Bunny Drop, and Cross Game.
Based on most of the others I think you should check out Madoka Magica, Penguindrum, Another, Fulllmetal Alchemist: Brotherhood, Chrono Crusade, and Mirai Nikki.
You might like The World God Only Knows.
Haruhi is a good anime, so I think watching it wouldn't be a bad idea. The only thing I'd point out, is that part of the hype of Haruhi comes from the experience of watching it as a community when it came out with all of it's zany meta stunts- for example: the first season aired all the episodes out of order.
Since you are new to anime I'd suggest watching various anime in different genre to see if you like them or not. These anime would include:
K-On
Shakugan No Shana
Crest of the Stars
Neon Genesis Evangelion
Maison Ikkoku
Ranma 1/2
Ah My Goddess
Soul Eater
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Cross Game - A Story of Love, Life, Death - and Baseball. What more could you want?
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