I started on the Led Zepplin Stairway to Heaven solo, as any self-respecting guitar player should. I'm a self taught guitarist, who branches into classical. Going the guitar course without a teacher is tough, no doubt about it, but don't let that stop you.
The first thing I did was find some tabs of the songs I liked, and worked them out, pretty painfully, on a fender squire. It sounds like you have a nice set up, I'm working on a 20 year old classical yamaha (worth about $100 on ebay).
The hardest part about guitar is getting your early finger muscles developed, as long as some callouses on your fingertips. You really have to have a passion for the instrument to stick with it. I found my learning curve to plateau pretty much all the time. You'll feel like you're going nowhere, but one day you'll wake up and be 4x better than you were yesterday, strange.
As for exercises, get those boring and lame scales down, because they make improvising so much easier. You can impress your friends by making stuff up on scales spur-of-the-moment. My entire scale practice goes (in numerics): 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1, 1 3 5 8 5 3 1,(triplets) 123 234 345 456 567 678 7898, 876 765 654 543 432 321 2101. That just helps warm you up. Get a couple simple songs down with arpeggios as well.
Music theory is a pain if you ask me, nobody really explains all the simple terminology a complete noob wouldn't know, so I floundered about for a couple months until I picked it up. This forum is a pretty good resource though.
Get a teacher if you can.
As for styles, rock is fun and easy if you want to jam with friends. Power chords (they have a basic shape and sound good on an electric) are quick, dirty, and awesome. I never got into jazz or blues except for a few basslines. Classical is where I ended up falling after a few months, and it's awesome. With classical you get to play both bass and melody, the guitar is the entire orchestra. I've been playing for about 7 months now.
Basically, if you can read music, GREAT! If not, go learn and get some tabs to hold you over. Pick out stuff you like, and work on it. There's a lot of nit-picky stuff about technique you probably know, but I never really let that bother me.
So, thats my music story, and yeah I'm as bad as I sound (bad pun).