Pet/fancy rats have gone through some breeding selection to try and weed out aggressive behavior (or at least bites). With that said, a wildie can be just as friendly, but you'll want to be extra careful to try and curb negative behaviors.

You can raise a baby rat (although it doesn't need to be a baby, too) found in the wild, because they are virtually the same as domesticated ones. At least here in Europe, where I live.

The type of a rat you're looking for is a "Norwegian Rat" or "Brown Rat", which is the most common type in the wild.

Generally speaking, there's a saying that animal you rescued will try to pay that back in love.