There are 3 main types of domestic rat.
~ Brown rat/Lab rat: Rattus Norvegicus
~ Black Rat: Rattus Rattus
~ Gambian Pouched Rat: Cricetomys gambianus
Depends if you want a big rat, medium rat, or small rat. The
Gambian isn't available everywhere. The Brown rat is a very common
one, & there's a few variations.
Do some research on each, & see which is of interest.