Do I have time to look after it?
This is a big one. If you don't have time to look after your pet - i.e. walk your dog, groom your cat or clean your rabbit's hutch regularly - should you really get one at all? Research what's involved in looking after the particular pet you want to buy and think about how you'll fit those tasks into you and your family's/flatmates' regular routine. If you work a nine-to-five job, it's also worth thinking twice before getting a pet that needs constant attention.
Can I afford it?
There are all sorts of hidden costs. First there are start-up costs (such as buying all the equipment, food and grooming tools required for your pet), then ongoing costs continuing throughout your pet's life (like regular vet visits, ad-hoc/emergency vet services, grooming products, food and toys). Research the average cost of all of the above and draw up a mock budget per year or month to see whether you can afford to look after the pet you want.