Hmm.
Well here's my generic answer to newbies:
under normal circumstances when starting out in learning a musical instrument, the crucial skills required for any musician is timing, rhythm, technical ability and ability to read music... and above all.. the ability to tune one's instrument by ear.
Now, if you would be able to attain the basic skills of timing, rhythm and technical ability I'm sure you'd be able to tackle alot of genres out there, not just rock or even it's subgenre visual kei.
What I would say is that learning acoustic is probably the best way because you would be strengthening your fingers (acoustics generally are slightly tougher for one to press down on the strings) and also by learning simple rhythms and tunes initially you would be learning from the ground up.. building the foundations for you to be fully ready to tackle the genre of your desire.
Not to mention, along the way you might be drawn towards different genres and then some.
And btw, with a budget of $200 you can get a decent beginner guitar, and in the 2-3 years you take to learn the instrument with adequate dedication, you could be able to save up for an electric instrument and hopefully get a decent intermediate instrument to help you on your way to guitar-god-dom.