Where do I start a new pet for the family? What is the ideal pet for the household? Good start by collecting information. This is key as a pet is for life, so if in doubt do not have one.
A bit negative there, but there is such a large choice of potential pets to choose from, all of them can be engrossing, but have different advantages and disadvantages. You can opt from a dog, cat, gerbil, rat, fish, rabbit, snake and the list is never ending.
It is important to involve everyone  in the assessment, it needs to be a complete family decision. Due to its significance I recommend you talk about and write down your aim for wanting 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 needed, ability to fuss, interest, shared activity, any phobias, other issues.
Pets take time, some require more than others. High maintenance animals are those that require regular exercise such as dogs and horses. Dogs evolved from wolves and maintain many of those characters. They are used to regularly covering large areas every day to search for food, so most dog breeds necessitate at least one to two hours a day walking. This should be part of a routine and done rain or shine. Others may require a lot of grooming, changing water etc. A cat sitter often uses  a lot of their visit to brushing long haired cats, though the cat and the sitter enjoy it. You may wish a specificpet, but do you have the time for him? Be honest with yourself and the prospective pet.
Expenditure, consider all costs. There is the potential cost of the pet to start with, which for a pedigree animal can be costly. I would like everyone to consider taking a rescue pet, there are more and more of these at the moment as families are unfortunately discarding them to the pet charities – why not do good and help out? The other set up costs include cages, leads, grooming aids, blankets / beds. After that are the ongoing pet costs, food, which for a large dog can be substantial. I strongly urge you to have your pet neutered, many pet specialists and studies have shown that you will have less behavioural problems with a sterilized pet. There are routine veterinary expenditure such as vaccinations, however some are impossible to plan for. For this reason I strongly recommend you to invest in pet insurance, so you can deal with any unexpected accidents that may occur. There are routine costs for flea treatment etc.  This expenditure rapidly mount up.
Is your house large enough for the pet? Some pets can be interesting, but you may not be able to fuss them, what is the crucial for you? No pet has everything. Can you pick up the pet? Rats are exceptionally interesting, but a few people hate the scaly tail, or the idea of one.
You may want to review the summary paper, do you have the time for walking the dog during the week due to work pressures, but this may pay for a professional dog walker. Not enough space for the horse, use stables, but watch the cost.
So once you have chosen a type of pet, there is often a huge variety of diverse types and breeds to decide on, looking at hamsters there are five basic types, with very different features. There is also the choice of numbers, some animals are better off single, others as a pair because they need 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 propose you to organise a pet test drive. Find someone with a similar pet, that you can look after 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 work that is needed, and do not forget the pleasure that the pet gives.  An alternative is to do some animal charity work. 
Pet breeders are exceptionally knowledgeable, so visit and discuss with them.
I hope this helps, go and enjoy a new pet.