Getting the best out of your pets
A beginning player will want to have Kit as one of their beginning pets as soon as possible, primarily the shop should have one in store. If not, you can always create a new account and try again until one is available. Diamonds will be easy to come by in your first few hours of gameplay.
Nova will be everyone's first pet, when you rescue them from Kage on stage 8.
Next, you will want to focus on getting all your pets to at least level 5, there are 16 pets in all to collect. This will give you a bare minimum passive for inactive pets. Your active pet will game 100% of its bonuses.
This little tip usually applies for levels 30-99. Past 99, is 100, which equals 100% passive bonus for your pet. Selecting the lower level pets usually will yield a stronger pet damage bonus. You can click each one, to see which one is giving you the most power. Therefore the pet with the weaker boost is usually selected as the active pet. If both pets are at the same tier of passive bonus, select the pet with a higher level. After all your pets have reached level 100, it does not matter which one you choose, you can now consider it your cosmetic pet to be by your side.
Pets eventually start to become your main source of damage around stage 550, however, depending on your artifacts, this could be more or less depending on artifacts.
Since 2.8, pet skill trees have become a great source of damage for early game players.