Actually pet rats can be very enjoyable. Folks get creeped out because they think of feral rats, but pet rats are not nocturnal, they will recognize you and be active when you are. However, their living space needed to be keep clean, it's normal for every living creature to expel waste. The rat can't clean his own space, so you have to do it. One word of caution, get just one, more than one and you may suddenly find you have 100.
Other than rats, have you thought about parakeets? I love birds but I no longer have any. I have dogs so it's not really safe for gerbils, rats or birds. I haven't checked on the cost involved in proper care for any of the small animals, but it's crucial to provide the right equipment to be a responsible pet owner. Without the proper care, a rat, gerbil or bird or even a reptile will sicken and suffer. Make sure you can afford to take proper care of whatever pet you chose. Because if you can't, the poor animal will not live a happy or healthy life.
Good luck figuring this out, I love animals, and I hope you can acquire a pet. It will be a lot of work as well as a ton of fun.
PS. rats won't fly around the house and chew the tops of drapes. And they won't poop on your TV, just a few things to think about.