Well right now I have two rats that have babies:
1 beige berkshire rex rattie (Goober)
1 agouti berkshire silk rattie (Gizmo)
When people come to me to adopt ratties, normally it is just like adopting a dog (without the breeds, people base them on color, markings, hair type, personality, and gender) they come in and look at each rat. They are allowed to handle the ones they are interested in, they look them over and choose which ones personality, color, etc. is most to their liking. Normally, I try to encourage first time rat owners to take two rats, as well as a booklet I have. Rats are very social creatures, so having two (I normally recommend a fixed male, and female) they will never get lonely. Loneliness can lead to depression, just like in humans rats need social interaction to survive. They seek this from everyone, their human and cage mates.
The most commonly adopted ratties are Rex's (they have curly hair that is thin, it is very soft to the touch - Rex's normally have curly whiskers as well) and hairless (rats with no hair) there is such a thing as a double rex (a hairless rat with patches of hair) but they aren't as common.