I do pet photography as a hobbyist on a budget with old gear for free at pet friendly charity events, generating donations for animal shelters and the like. Usually aiming for very clean and optimized printworthy shots, as that is the most useful thing for petowners used to smartphone shots of their animals.
My weapon of choice is the Canon R with either the amazing 85mm Viltrox, the Nifty fifty or the EF100mmL.
f5.6 or smaller to get the whole head mostly in focus, aiming at the eyes. Of camera 4-way lighting and a bag of treats. Backdrop is a cheap one from ebay, selectivly lit to force a contrast between rim lighting on the left and backdrop for a more 3d effect. All images are heavily edited and stylized to approach a previously set look.
The theme i aimed for at the most recent event was "Old Portrait Paining". Attached is a resulting pic.