I dont know? Which album should I check out first?
You really can't go wrong w/ the Pixies. All are great. Doolittle is probably their most popular album.
I used to listen to a lot of indie stuff, but not as much over past couple years. I'm glad to see you mention Slint. I've recommended that album a couple times here, and I couldn't get anyone to bite.
Jeff Buckley was amazing, and My Bloody Valentine is/was great too, but I know a lot of people are into them. I haven't heard The Shins' new one, but their first two are both quite good. Never really got into Sonic Youth.
Some stuff not mentioned:
Pavement - Slanted and Enchanted
PJ Harvey - Dry
PJ Harvey - Rid of Me
Guided By Voices - Bee Thousand
Guided By Voices - Alien Lanes
Janes Addiction - Nothings Shocking
Radiohead - OK Computer
The Cure - Shit, most anything, but especially Pornography & Disintegration
There's a bunch more if you already know or aren't interested in those. Let me know if you want more info on any.