You may wish to consider a chinchilla. They are in the rodent family, (but it doesn't seem that way). Chins have incredible velvety fur, and they resemble a chubby squirrel with Micky mouse type ears. They are nocturnal, although they do get up and play a lot during the day. Chins are very smart and playful, and I'm told can be trained. They are also very clean, so their cage area doesn't tend to stink as many do.
I got my first pair of chinchillas, as adults, a proven breeding pair. They were nice enough but they never really did bond with us. We ended up having 3 litters total. They usually have 1-3 babies, and their pregnancy is 111 days (about 4 months), which is VERY long for an animal that size. The babies come out fully formed, "ready to go" you might say. Fully furred, eyes opened, running around. They can even eat adult food almost from day 1, although they prefer to nurse.
Chinchillas eat prepared chin food that comes in a pellet form. They also need 1 raisin a day (which they LOVE!). Every few days it's a good idea to give them a dust bath, you can purchase "chinchilla dust" at a pet store. You put it in a bowl and they dive in, roll and kick up a fuss, a pure delight to watch. Company always love to watch "Ittle bittle" take her bath.
The real joy for us came as we kept one of the babies, we later sold mom and dad. She bonded really well with us, she was handed a lot from birth on. She has been one of the BEST pets I've ever had (of any kind of animal). She is playful, friendly, never bites, she "barks" its a quiet, cute kind of bark. A whole lot of personality and character she is.
Chins are more playful type pets, than a sit down and lap type animal. I would recommend getting a baby if you decide to get a chinchilla. They usually run about $100. in the US for a pet, but that price can vary a lot.
Another very nice quality about chins as pets, is they have no claws or fingernails. They have these little soft pads on the bottom of their feet, so you don't get scratched. I wouldn't recommend them with small children however, as young children could easily hurt a chinchilla.
They have a life span of about 25-30 years. They do need to live indoors, or climate type controlled setting. Chins come in a variety of colors but the standard grey color is the most common, and the other, more rare colors will cost more usually.
I found when I was trying to sell the babies, that most people had no idea of what a chinchilla was, or had even seen them. That made it a bit difficult to find homes at times, although with such few babies, it wasn't a problem. The people who did come to purchase the babies had this one thing in common: all of them had either owned a chinchilla previously, or had a close friend who did and had been around them. That really says something about this type of animal for a pet. You can check out your local pet store for chins possibly, or the internet.