The 38 snubby is a great gun, but the blast and rather lively recoil might scare your daughter even more. Make SURE she has excellent hearing protection before you fire a handgun around her. In my experience most newbies are more intimidated by the noise than by anything else.
As for the poster who said you need a man, he was partly correct. You would do well to find a friend who is a shooter who could take both of you out and show you the ropes.
A class is always a good idea. If SC's CCW law requires a training course that might be a good place to start. Hunter safety courses are also excellent for learning safe gun handling. It doesn't need to cost a lot.
If nothing else ask around at the local gun shops to find out what kind of training opportunities are out there in your area. Shooters are generally a helpful bunch so I'm sure you won't have too much trouble getting help and advice. Just remember that any recommendations you will get on guns will probably be based a great deal on individual preferences, and you will maybe never get the same advice on which gun to buy. Do your homework, and try to get your hands on and shoot as many different guns as you can before you buy.
My advice is to start small and work your way up. A Browning Micro Buckmark semi-auto in .22 LR would be one of my top choices, or a quality .22 wheelgun if revolvers are your thing. The important thing is you want a gun capable of decent accuracy, low recoil, and with good sights so that you can put your shots on paper and develop good habits from the start, rather than devloping a nasty flinch and being disappointed because you can't hit the broad side of a barn.
My first handgun was a .44 magnum. BIG mistake... I flinched terribly and could not hit anything with it. Well I finally went and bought a .22 and spent a lot of time shooting it. After that I was able to shoot any handgun accurately and well, including the .44...
And a .22 is loads better than nothing when it comes to personal defense...
Anyway, good luck and welcome to the shooting sports. I just woke up, so please excuse my lousy writing style...