It was sort of a weird progression for me, with a few starts and stops.
My father has an old Silvertone archtop acoustic that he bought for I think $20 in 1960 (he was 12), because he wanted to be a singing cowboy, like Roy Rogers or Gene Autry. I banged away on it a little when I was a kid but I wasn't really interested in playing guitar until I was a teenager. I had been taking piano lessons since I was 7, and started playing trombone in band in 6th grade. For some reason I wanted an electric guitar when I was 12 or 13. I wanted a black Strat from the Sears catalog so bad, but I couldn't tell you what triggered that desire. Looking back on the music I was listening to at the time, it was 1989 and I hadn't really gotten into hard rock yet. I just had it in my head that the electric guitar was cool. I'm also left-handed so I thought I wanted a left-handed guitar, but was convinced to learn to play right-handed (still the smartest piece of advice I've ever taken when it comes to music). I ended up buying a black Strat copy made by Arbor at a garage sale probably that year or next, along with a Marshall Lead 20 amp.
It sat neglected for a few years because I couldn't make it sound like I wanted it to. I didn't know anything at all about distortion, overdrive, or gain. I knew when I turned the gain up on the amp it got louder, but because it was *too* loud for playing indoors I never did get it loud enough to break up.
For the next couple years I got into 70s folk-rock. James Taylor, Simon & Garfunkel, and so on. At some point I pulled out my mom's old LP version of American Pie by Don McLean, and decided I was going to learn how to play that song.
I started on my dad's acoustic but quickly went out and bought my own at the local pawn shop (the guitar itself was not used; it was a new but cheap catalog import sold by a fellow who had set up a small music shop in the back of the store). I paid $60 for it, and, armed with a chord book, I sat in the garage in the back of my parents' 1985 GMC Safari minivan, doors wide open, and listened to that song over and over, figuring out the chords and teaching myself how to play American Pie.
Then a friend showed me a distortion pedal, and everything suddenly made sense. After that, I decided I would try to tackle Stevie Ray Vaughan's "Couldn't Stand The Weather," on my Strat. It all blew up from there.
If Don McLean inspired me to start really hunkering down and learning how to play, Rush was the band that made it stick. Another friend had me listen to "Chain Lightning," from the Presto album... and Rush quickly became my favorite band. I picked up an enormous book of music ("Rush Complete") and learned a bunch of their early work. I bought every guitar magazine that had one of their songs in it. The guy who introduced me to Rush soon became my first bassist, and along with a drummer I recruited from marching band, we started our first band. That was the point at which playing the guitar was no longer a temporary hobby to be discarded and forgotten, but a long-term project.