Where do I start a new pet for the family? What is the best pet for our family? Well you are starting well by collecting information. This is key as a pet is for life, so if in doubt do not have a pet.
A bit negative there, but there is such a wide range of potential pets to pick from, all of them can be exciting, but have diverse advantages and disadvantages. You can opt from a dog, cat, gerbil, rat, reptile, rabbit, bird and the list goes on and on.
I can advise you to involve everyone  in the choice, it needs to be a complete family decision. Due to its significance I recommend you thrash out and commit to paper your objective for desiring a pet. Add to it on a large sheet of paper, with a column for the pet, some columns to rank each pet. The considerations for a pet include, time (yours), cost (pets are expensive), pet care, space constraint, aptitude to fuss, interest, joint activity, any phobias, other issues.
Pets take time, some have need of more than others. Time hungry animals are those that require regular exercise such as dogs and horses. Dogs originated from wolves and maintain many of those characters. Searching for food they walk many miles to search for food, so most breeds have need of at least one to two hours a day walking. This should be part of a routine and done everyday. Other animals may have need of a lot of grooming, changing water etc. A cat sitter often uses  much of their visit to grooming long haired cats, though the cat sitter and cat enjoy it. You may hanker after a specificpet, but do you have the time for him? Be candid with yourself and the potential pet.
Expenditure, think of costs. There is the purchase cost, which for a pedigree animal can be steep. I would like everyone to think of adopting a salvage pet, there are increasing numbers of these at the moment as people are unfortunately discarding them to the pet charities – why not do good and help out? The other starting costs include cages, leads, grooming aids, blankets / beds. Then there are the regular pet costs, food, which for a large per can be substantial. I strongly recommend you to have your pet sterilized, many pet experts and research have indicated that you will have less behavioural problems with a neutered pet. There are routine vet expenditure such as vaccinations, however some are impossible to plan for. For this reason I strongly recommend you to take out pet insurance, so you can deal with any problems that may occur. There are routine costs for flea treatment etc.  This expenditure rapidly mount up.
Do you have the space for the animal? Some animals can be watchable, but you may not be able to fuss them, what is the most important for you? No animal has it all. Can you handle the animal? Rats are remarkably exciting, but some individuals do not like the scaly tail, or the idea of one.
You may want to revisit the summary paper, you may not have the time for dog walking during the week due to work pressures, the upside is you have the money to pay for a regular dog walker. Not enough space for the horse, use stables, but watch the cost.
So finally you have chosen a type of animal, there are lots of diverse types and individual species to decide on, looking at hamsters there are five basic types, with very different characteristics. There is also the choice of how many, some animals are better off single, others as a pair because they require the company. Then there is what sex, some pets have very different behaviour between the male and female. Male rats are less active than females and urinate more.
After all of these decisions, I would recommend you to take the pet for a test drive. Find someone with a similar pet, that you can borrow for a few days, or even be a pet sitter for them for a couple of weeks during the holidays. Discuss with the owner about the expenditure, the effort that is needed, and do not forget the pleasure that the animal gives.  An alternative is to do some pet charity work. 
Pet breeders are extremely knowledgeable, so visit and talk with them.
I hope this helps, go and enjoy a new pet.