Hi M.,
Sorry for the late response, but I had to put my two cents in since this subject is dear to my heart. I have had hamsters, rats and bunnies and a childhood friend had guinea pigs. I am so pleased to see so many responders lovin' the Rat! They really are the best; much, much better than the hamster or guinea pig (and definitely forget about mice. I think they only sell them to become food for peoples' snakes!) Rats are smart and clean and affectionate. They are also very easy to take care of, much easier than rabbits. You can leave a bowl full of food and a full large water bottle for a rat and he'll be fine for many days if you have to go away, but rabbits will eat all their food in the first day! In addition, rabbits pee and poop ALOT, so you'll be cleaning that cage a lot more often. Granted I had big rabbits and, by comparison, the rats were small, but still....! It was ridiculous how full that litter box got.
I wholeheartedly agree with the poster that recommended getting a white lab rat instead of a fancy rat. Although there are several common breeds of lab rat, the BEST is the Sprague Dawley. According to wikipedia, they are "known for their calmness and ease of handling." I have had fancy rats and my one Sprague Dawley and he was, by far, the best. He was SO sweet! Just a dear. I recommend getting one as a pup and then handling him or her every day. Then they will take to and thrive on the physical cuddling. Unlike other rodents, I think you can have more of a relationship with a rat, more like you would have with a dog or cat, because they have real personalities.
The only drawbacks to rats is that they do not have very long lifespans and their proneness to non-cancerous mammary tumors. Both my fancy rats had to be put down due to tumor (it grows to the point of impeding movement, at which point I elected to euthanize), but the Sprague Dawley appears to have just died peacefully in his sleep of old age (at about 3).
I have never had chinchillas, but that previous post was interesting. Looks like they might also make good pets, but 15-20 years is quite a commitment. Of course, you won't have to jump into the whole death and dying conversation quite so soon!
Good luck in whatever you decide is best for your family and enjoy your new pet!