I started out with an acoustic (in fact, that’s the only type I own, but when I can get my hands on an electric I rip on that, too). The first song I ever learned was “Blowin’ In The Wind” by John Denver. I learned that one from a chord sheet in five minutes and had it memorized the next day. That was just strumming, though.
I worked out my own method of finger-picking (kind of like a banjo roll), which is what I usually use because chord-strumming seems so, I don’t know, plain. The first song I ever learned to play EXACTLY like it is on the recording, using a variation on my style of finger-picking (which is actually completely different, since I’m imitating exactly what’s on the CD) was Garth Brooks’ “The Thunder Rolls”, which is still my favorite song to play.