My last furry pet was a rat, about 5 years ago. I adopted her from some acquaintances who couldn't take care of her. Before I got her, her last owners just let her sit in her little cage 24/7. She had a grumpy and mean personality. But after I adopted her, I started letting her out of her cage for play-time and interacting with her a lot, and she became one of the most personable pets I've owned, no exaggeration. Like a dog or cat, she loved to be petted and scratched behind her ears.
So I'd recommend a rat, with the qualification that you have to be prepared to spend time with it, give it toys to play with, and generally keep it stimulated. Because they are so smart, they get bored easily and can turn, like I said, grumpy and mean. It can be good to keep a pair of same-sex rats, and that way they have a constant source of social interaction.