First of all,
Acoustic or electric?
Keep in mind that with an electric you'll have to get some sort of an amp (you can get pretty cheap ones, but they're kinda useless once you get good). The electric is a bit easier, but the acoustics are a bit cheaper for the same quality, you don't require an amp, and they teach you a little bit better (electrics cover your mistakes a bit better).
I'd suggest going with a Simon and Patrick acoustic first, then after a while, going up to an Epiphone electric (Les Paul mmm), as they're pretty cheap still. You can then slowly upgrade the Epi with new pickups etc and end up with a near-Gibson quality Les Paul electric.