What type of pet to get?

I want a small, inexpensive pet that likes to cuddle, but we can find, like, nothing. We aren't getting a dog or a cat, and we definitely won't be getting a rat or a snake. No birds, that's ruled out, even though I'm sad about that. We're keeping sugar gliders and chinchillas as an idea, but we also won't be getting a bunny or a guinea pig because they can really be thought of as prey, and we've got 2 dogs and we aren't sure how they'd react. Any other suggestions?