Well, I first got into indie through Bright Eyes. But he's not only a bit weird, but if you want any indie cred whatsoever... I'm pretty sure you're not supposed to listen to him

Next I started listening to Hot Hot Heat and Mae pretty much simultaneously. Kind of a weird combination, but eh. I
love Hot Hot Heat (but not so much their newest CD...) but I can only take Mae in small doses. Some of their songs make me super-happy, and some slightly annoy me. After that came The Postal Service, which I loved and...
Then I tried out The Unicorns and hated them.
Then I tried out The Pixies after somebody made fun of me when I didn't know who they were. They took some getting used to.
After that I went into an indie immersion of The Decemberists, Belle & Sebastian, the New Pornographers, and a whole bunch of other bands that have already been listed so I won't bother naming them.
Last week I tried out The Unicorns again and loved them =)
I'll never be a true indie kid. I am not nearly pretentious enough, and I still listen to "awful" music. But I figured I'd share my own experiances.
My main advice is if you don't like something the first time... go back to it later! Chances are you might just need to get used to it or maybe try them again when you're in a different mind set. Just be careful not to let the music suck you in too hard. Indie music seems to have the power to turn you into an elitist prick like ASturge

(Just kidding about the last part, Sturge.)
(Well, okay... only
half kidding...)