You have a lot of choices. First, accept that any pet will require some level of care. Before making an impulsive decision, understand the level of care, lifespan and diet / environmental requirements for that species. Also, make sure you have the required space, funds and time to properly care for your new addition. Owning a pet can teach younger children responsibility; interest may wane. As parents, you must be prepared to take over that responsibility if this happens. Books, veterinarians familiar with exotics, pet store employees, other pet owners, online forums and groups, and websites can be very valuable sources of information and are good places to start. Make sure you are dealing with someone with knowledge of exotic pets.
Know yourself. Are you a night hawk or a morning person? Many animals are quiet during the day but active at night. What is your tolerance to noise? Birds and dogs are noisier than snakes. Will you want to cuddle with your pet? This could be challenging to accomplish with a hedgehog. Consider the diet of your pet. If you cannot imagine feeding insects/small prey then some pets will not be appropriate. Understand the social structure of the species you are considering. Two male rabbits will not get along and some species (rats, for example) are very social. Finally, if you, or anyone in your family, have allergies, a fish or reptile might be a better choice.
If you think a rodent is a good match, consider rats and guinea pigs. If you are interested in a reptile, a corn snake or leopard gecko is worth considering. For birds: cockatiels and budgerigars are good choices.
A lot of people acquire pets they do not keep and many pets (exotics included) are relinquished to humane societies. Please consider rescuing as an option.