This would probably get more knowledgeable responses in pet general.

I've pretty much had it all at one time or another. A lot of others on PT have too, you'll be more apt to find them in pet General though.

Fish are nice to look at but that's about it. I've never been too big on fish, though I know a lot of people here do really like them.

Hamsters aren't too hard to care for, but they aren't always the nicest of pets. I've had very easy going hamsters and very nippy hamsters.

Gerbils- I've not actually had one myself, but my husband had one when we were dating. I really liked the little guy, but he was really fast and hard to hold on to.

Guinea pigs are more work than smaller rodents. Mostly because there is more cleaning. I cleaned them daily as opposed to weekly for the smaller rodents. They of corse also need a larger cage than a lot of other pets. They tend to be very sweet though.

Rabbits are great, but they too need a larger cage and males often spray. They're no too difficult to litter box train though (I suggest a covered box).

Ferrets have always been a favorite of mine. They do have an oder though. They aren't too hard to care for but aren't the easiest either.

Chinchillas- I absolutely do not recommend a chinchilla. I love mine dearly, but they can be a rather difficult pet.

Rats are also one of my favorite rodents. They are a great pet to play with or to sit and watch TV with.

Mice are also a favorite of mine. Because of their small size they are less cleaning than a lot of other pets. Their cage also takes up less room. They're generally very sweet and easy to hold.

Cockatiels are probably my favorite small pet. Birds aren't for everyone though.

Budgies (parakeets) are also great, though I prefer cockatiels.

Most reptiles I don't recommend for kids (though 13 isn't really a kid anymore). Reptiles needs are often more challenging. I've never had a leopard gecko but from what I know of them they aren't too difficult and are generally a good starter reptile.

I don't know your family's situation with the divorce, but if there's any possibility of a move (especially to a rental house or apartment) I don't suggest a dog or cat.

If you have any questions please PM me, I'll be happy to help you if I can.
Good Luck!