Or should I not accept any pets at all?
Best not to allow pets but if you do it is better to increase the monthly rent by $100 than to charge a one time fee or deposit. This will discourage pet owners from applying but make them pay a premium if they do.
Having a pet in a rental is a privilege that they must pay for.
people love pets, wouldn't worry much if you have tile/wood, carpet is the worst. Charge a fee, the pets are going to leave their mark. I've charged as much as $500.
I would definitely charge an additional deposit and a monthly pet rent/fee. A pet will cause damage, even if it's only staining the carpet or making brown spots on the lawn. These are areas you will want to fix after the tenant moves out and it's easier to use a pre-collected pet deposit than rely only on the security deposit. As for the pet fee, pet-friendly properties are a premium amenity that renters will pay for. That fee suddenly becomes additional income, whereas a pet deposit will have to get returned if unused.