It is extremely important that you ensure that it is from captive-bred stock and that it has not been imported from abroad. Find out everything there is to know about the species you are thinking of. Buy a good care guide, talk to your vet, surf the net and contact other people who have the same pet to find out the pros and cons. If it needs regular exercise, make sure you can put aside enough time each day. Tarantulas may bite if they feel threatened and release hairs that can irritate your skin and eyes.
Some amphibians can also be difficult to handle due to their coating of protective slime.
It may be difficult to find a vet who has experience with exotic pets. Find out if there is one local to you. Children and exotic pets rarely mix. Some species are potentially dangerous to people and other animals. If you have other pets, be sure that they will get on with an exotic species.