As previously stated, pet people come in as many breeds as you can possibly think of. By far and away the most popular are the dog and cat types, but exotic birds and lizards have been gaining popularity among trendsetters from L.A. to Tokyo!
All pet types are best suited for certain jobs, and when hunting for one, it is best to search for a type that suits your needs best.
However, a "True Match" - when a pet person bonds with you and only you for the rest of their natural lives - comes naturally, and sometimes takes time before you can find the pet you will be able to give a forever home to.
According to all current research, pet people are completely sentient and like us in many ways. However, it is important to remember that they have many animalistic and feral characteristics. Do not be foolish and think that your pet is a person, despite the facts that many are clothed and may be allowed to read, write, and have "hobbies." Some traditional pet owners may eschew these frivolities, and that is within their right.
Pet people age more quickly than humans, at least physically, and many types have long lifespans. It is not uncommon for pets to be passed through the family. When getting your child their first pet, it's important to keep in mind that just because the pup is tiny now, a grown pet can be jumpy around a small child.
It is important to train a pet. Discipline will be necessary. This does not make you a bad owner. Failure to train early will result in a rebellious pet. Training is especially important if you want your pet to serve as a household servant.
Remember, your pet will be extremely protective of you, especially if you are Truly Bonded. It is best to socialize them early. A socialized pet is a perfect family pet.
These days, unowned and unbonded pet people are allowed to live as strays or "Frees" in certain designated areas. Some even hold "jobs." This is against their best interest, and owners who adopt these strays are to be rewarded. Still, the best place to get pets are from liscenced kennels or breeders.
Some masters find it beneficial to participate in activities with their pets, such as shows and other competitions.
Finally, much has been made about the sexual relationship between pet and master. This is a normal facet of the bond, and humans are sure to find pet people sexually alluring. But beyond that, it is only responsible and prudent for owners to care for their pet's needs. It is a well-known fact that the libidos of pet people are remarkably strong, and when they go into heat, it is usually more convenient for a master to relieve them. There is no risk of pregnancy. All rumors of hybrids are urban legends.
Despite this, masters must remember to not view their pets as romantic partners. Humans should stay with humans.

Comment with your character and say whether they'd be a master or a pet. Ideally, they could be played as both. Mention what kind of each they'd be and what they'd be like, (ie: "Xx-chan is a bunny girl who is happy to please her master" or "Asterothia is a cat boy who is aloof but loyal to his true master"). For pets, be sure to include features ("wolf ears, tail, teeth).

REMEMBER, pet does not automatically equal submissive and master automatically equal dominant. This is not a BDSM setting though BDSM can be included. How far you want to go with the actual "pet" aspect is up to you, as well. Your pet could just be your slightly-furry roommate or soulmate!
Comment to others.
Play out the scene.

First Time Pet/Owner: Usually, pets are gotten at a young age; you're an old dog. Can you learn new tricks?
True Bond: What all masters and pets yearn for...the pet's loyalty and adoration for life.
Love: It's expected for masters to love their pets, but to love them? Romance is strictly forbidden.
Old "Couple": Master and pet have grown together and know each other. You know, know each other.
Loss of Master: The pet has lost their master, perhaps even their True Bond. Is it possible to move on?
Young Master/Older Pet: Pets age quicker than masters, so it's possible to end up with a bit of an "age" difference.
Family Pet: This pet's been raised as part of the family. What happens when their feelings for a family member get more than platonic.
For Your Protection: You don't want to be a master, but you have to take in a pet for their protection lest they be in danger from the general public.
Stray: You're a stray or a "Free." Can you live like this with your biology screaming for you to make a match?
Servant: You're more servant than pet.
All Sex, All the Time: The only purpose for this pet is to service the master, and not in a way that means cleaning their house.
Guard: You're a loyal bodyguard, a service pet. You'll do anything for your master. Anything.
Pet Play: This is for those who prefer to keep their animals on leashes, have them eat from bowls, and keep away from clothing.
Breaking In: Training is important with any pet.
In Love with Another Master...or Pet: To lust after another's master is no better than treason, and to wish to be with another pet just cruel!
Punishment: Bad dog, no nookie!
Heat: All pets go into heat, and it's the responsibility of the owner to take care of this problem. After all, unchecked dry humping kills thousands every year.
Breeding: Breeders know the best qualities in each type and mate the cream of the crop together to continue lines. It's a hobby for some, a calling for others.
Territorial: Hey, hey, other dog person! This is your apartment. Stay the fuck out!
Kennel: Kennels are where unadopted pets are kept. They're generally agreed to be depressing places. Why not volunteer at one, keeping the pets healthy and happy with the kind of affection only humans can show?
Rebelling Against the System: Damn the Man! Pet people are people, too! Just be careful not to get talk. You know what happens to bad pets.
Instant Attraction: You ever just look at someone and know they're the one? That they're...your master? But what if you've been trying to fight it? Well, don't try!
Dominant Pet: You might be the pet, but you call the shots, at least in the bedroom.
Pet Show: Everyone wants to show off how perfect their animal is. Look at that ass! And you'll never believe their special skills...
Therapeutic: Pets, especially those bred for their kindliness, are perfect therapy for those who've been through trauma and heartache.
Jealousy: Who's that around your master? Oh, hell no. They better not be touching them!
Petting: Pet people are absolutely gaga for being touched. Even the most steely ones turn to mush for rubs.
Games: Playing with your pet and giving them exercise is a key to happiness. Of course, with a pet person, you might want to use other toys instead of a ball.