american idiot is greenday, right? Well, if you're unlike me and actually like that crappy punk-like wannabe band, their music is extremely simple. If you practice, you'll be playing the song in less than a year. A $100 guitar will do anything a $5000 guitar will do, its just how well it sounds.
With your viola background, I bet you'll write some nice stuff in the future. If you listen to some of metallica's best songs(justice for all), you definately hear hetfield's classical training. But for starting out, $100 guitar is all anyone needs. Everybody starts there. My senior year in HS, I bought a custom made Carvin for about $1100. My first guitar I got for $100 was a Bentley.(no, nothing like the car) It's in pieces right now because I'm refinishing it again along with another body.
Oh, are you looking at electric or acoustic? Just go to a local guitar shop like a Sam Ash or something and pick out a cheap guitar, or even check the pawn shops. And tell your dad that guitar can do a lot more than rock music, but you'll still play viola. And if he doesn't believe you, I'll record my beethoven on guitar for ya.
Sam Ash has a Squire Bullet guitar for $100. (samash.com)
"eureka" - Archimedes