My hands too small?

This guy lent me his Mexican made Stratocaster, I thought I'd learn to play.
I don't know the termininology, but the neck is about 2 1/8 inches wide towards the bottom. Now this guy is about 6 foot 3 and big boned, so he has not problems getting his fingers around the neck. Unfortunately though I have hands about the size of a 13 year old, and I'm 29! Is this going to be a handicap for me? Do guitars come in different sizes? I can't really make any judgment yet because I don't know how to play anyway.

I was also thinking about learning the bass, as silly as it may sound, I like the narrow necks on them!

My guitar teacher always keep trying to get me to move my thumb behind the neck as opposed to on top of it where it is more comfortable for me. I have kinda big hands so I didn't really see the need but I have noticed that when I do drop my thumb behind the neck my fingers land allot more cleanly on the strings.
It is uncomfortable, but I think I will get used to it over time.
The reason I mentioned this is because I think that with smaller fingers it would be easier to get used to playing this way. (JMHO)

Having small hands it's just the oppisite.
i feel very comfortable with thumb behind the neck, but when I try to hook it over the top it's nothing but trouble.
But i think the main think is practice.
Every time i Learn something new I think "crap i'm never gonna learn this" or "how the hell am i supposed to stretch my finhers like that" a week(sometimes more) later i got it down.