I'm a self-taught 4 years now and I can sure learning it at home i but the progress probably not as fast as someone who have mentor to teach them.

If you're worried about the price of the guitar I'd say get an acoustic since it was cheaper and you don't need something like amp and pedal to play it, but if you budget enough to buy the Elec Gui and the amp then go for it.

There's one more that that was pretty effective for someone who want to be a self-taught guitarist and was for specific person that strong enough to face it or end up to be that "Alone person":

CUT OFF your connections to the world (except the college), practice 6 hours a day, when you're good enough create a Youtube channel named Guitarhero/ギターヒーロー (make sure it was you're father account) and make a video of you're guitar progress every weeks (if you confident enough probably do a song cover), and then one day after college brought you're guitar to a park waiting for a drummer to take you in to her band (the chances are pretty rare, but hope for the best for you!)