Just a quick response til I can hop on my computer and post some links...
Lenses:
I've learned the hard (and wasteful) way that cheap lenses generally aren't worth the investment. Now, not all cheap lenses are bad, but those eBay bundles of "wide angle" lenses for like $50-$100 that come with a ton of different things are junk.
Hopefully Geoff posts up as he has a crop sensor camera and has quite a few lenses for it. IIRC, he has a 10-20mm wide angle that takes great pictures.
I'm on the photoforum (iirc that's the name, I'll check and edit if needed). I don't post at all, just lurk and read. Most of the people there are professionals or extremely experienced hobbyists that are just insanely talented.
I like Ken Rockwell for product reviews and comparisons. He is very thorough and honest in his reviews.
As for a tripod, if you aren't gonna be taking a lot of landscape photos or long exposure pictures, I'd hold off for now. Any crookedness can be fixed on a computer.
As far as the different modes, manual is the best. It offers complete control over your camera settings. What I would do is this:
Take a bunch of pictures in auto mode. Find some that you like. Right click on the photo and click properties in the computer, or just click the info button on the camera. That will give you the exif info, which is the nitty gritty details about how the picture was composed. Then, after finding what pictures came out great with those settings, go to manual mode. Set the camera to similar settings and take some more pictures. Then mess with one setting at a time and see how it affects the picture. That's a great way to hands on learn what the different settings do.
Of course, reading on the subject is great as well.