So, following some advice I have received, I have decided to start releasing my excess pets. However, there are many factors that I feel I should consider when it comes to keeping and getting rid of pets. What are the most important things that I should be looking for when choosing pets to keep. Do I work off of aesthetic, or the number of traits, and should I worry about genetic testing at all?

I like to say that I won't release it if it's a tagged (not a purebred) themed, I just like it/have certain attachments, it has restricted traits, or is 6vis and a project pet (aka is usually infertile)

but it's still up to you

To be honest, it all depends.

Why are you keeping these pets? Are they for you, are they for breeding, for a project, for sell?

If they are for you, work off aesthetics. Do they make you happy to look at, no matter their number of visible traits?

If they are for breeding/projects, work off traits. Do they have the traits you need for your breeding project.

If they are for sale, work off traits and them being themed and the species. Some species are more popular, and the 'fabled' species tend to be worth a bit more. It also depends on how they are obtained. Brewing pets, from this festival, might be worth a bit more than caught pets. Themed pets tend to be worth more than non-themed and 'gen1 pets' tend to be worth more than offspring pets, unless it is a project pet such as a six visible or max stat.

Also, it is a good idea to do genetic testing, if you can, on all pets, but not really mandatory. Genetic testing really only lets a player know whether the pet has carried traits or hidden traits. All visible traits will be obvious when the pet is grown.