SGs have tiny necks and are pretty easy to play, plus you have tons of high fret access. Their necks are notoriously weak though - ask KimJongSick on this very forum. I've not played one in a while because they don't agree with me so I don't know about their sustain.
This isn't entirely accurate. The HEADSTOCK is what's notorious for breaking on Gibson instruments, not so much the neck. The SG's neck joint problems were fixed years ago, even if I still wouldn't entirely trust the joint due to the location of the neck pickup hole.
OP: I'd suggest just going to Guitar Center and playing shit until you find what you like. Personally, I'd definitely suggest a Telecaster. Simple controls, extreme versatility (the famed Nashville session guitarist Brett Mason has a vintage Tele, and all of Led Zeppelin I was recorded with a Telecaster) and they're none too expensive. Retrofit it with DiMarzio TwangKing pickups and we are talking about some SERIOUS GODDAMN TONE with none of that obnoxious single-coil buzz.
If you're looking for even more tonal versatility (and you happen to have something like $600), I'd suggest a Fender Deluxe Players' Stratocaster. It has the option for every possible pickup combination with 3 pickups (*fapfapfap*), has the classic Strat look, and if you retrofit it with locking tuners, you'll have complete tuning stability even if you divebomb the shit out of it with the whammy bar.
I've got a 2006 Squier Bullet, which is basically a thinner-bodied hardtail Strat. The model's been discontinued, but Musician's Friend still sells them with small Marshall amps as a starter package. Simple guitar, cheap, and plays like a dream. And Marshall amps tend to cancel out any single-coil hum, in my experience, so that's really a great option.
If you get a Gibson, get something with '59 humbucker pickups in it, because I am of the opinion that those are absolutely some of the best-sounding humbuckers available in the world. The Gibson warranty is a lifetime materials and labor warranty and their customer service people aren't douchebags and will actually answer the phone if you ever need to call.
Epiphone has some damn nice semi-hollows (I should stop masturbating over them) that are relatively inexpensive, and they also have a bunch of decent Gibson copies (they're licensed and owned by Gibson, blah blah). The Gibson versions of stuff are better sounding, looking and playing, but the playability and sound of Epi can be really good if you get lucky. For these guys, if you're buying an Epi-only model, you'll probably be okay, but if you're getting an Epi-made Gibson copy, play the guitar first before you buy it.
My experience is really limited to Gibson, Epi, Fender, and Squier electrics, but hopefully this info will get you somewhere. Best of luck to you, electrics are rad.