A mouse is a good pet for somebody who does not have a lot of time to spend with the pet. Mice prefer to be left alone...they don't care much for social interaction. I used to have a mouse, and I only bothered him once a week to clean him (during the week, I'd slip treats in by him, but that was it). He enjoyed our little bit of time spent together, but then he was just content to be left alone.
Rats are a lot more social...they require lots of interaction to be happy. Some rats get pretty big though, so you have to be sure you have enough room for them.
Right now, I have a hamster. He kinda likes to be left alone too, but he is very friendly and will play with me. He's a black bear hamster, which is a type of Syrian hamster that is specially bred to be gentler than most hamsters (they cost a little more, but it really isn't much...I got mine for $20). I've found that to be true...I've had a total of 7 hamsters in the past, and Benny (my black bear) is the nicest, sweetest, calmest one I've ever had.