All pets require care, can get sick, injured, can turn nasty (rats, gerbils, hamsters) and a fish tank requires constant care and money. I've had all of these as pets. Only pets I wouldn't let my child have were snakes. Even birds require attention although having pairs of parakeets as my first pets after moving out on my own was a delight. (If two parakeets don't get along it can be a disaster so one has to create a loving match.)

Alternatively, without pets, volunteer where there are animals. I volunteered for a few years at a therapeutic horse ranch, and I learned that horses are perhaps the most superior animals when it comes to sensitivity and empathy. However, big horses can be scary and you need a good horse teacher if you haven't spent time around horses.

When we first got married my ex bought me a hermit crab, which isn't supposed to be a good pet. However, we ended up having him for several years and he changed shells (his house) several times.