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. Exotic pets have specific dietary requirements, and may need to be fed with foods that you feel uncomfortable handling, such as frozen mice or live locusts. It may not be as easy to find a willing pet-sitter for a tarantula than for a kitten.
Some species carry diseases.
Reptiles, for example, can harbour salmonella. Find out the maximum size that the species you are considering can grow to. Some pythons can grow to over 6ft. The cost of accommodation, food and vet bills is likely to exceed the initial price of the pet, so think carefully about whether you are prepared for the expense. Some species become stressed if kept alone, whereas others will prefer to be solitary.