Our TAR lease clearly state that the deposit is not last month's rent. We routinely set our deposit amount above the rent amount intentionally, to encourage the resident to keep the place in good condition & to remind them that is separate from the rent. The hope is also that they have skin in the game which hopefully incentivizes them to keep the property in great condition. Make it clear that unpaid rent will be sent to collections and all late fees will apply which will make it even harder to rent another place in the future.
As has been mentioned earlier, the pet deposit is critical but also pet rent. We have a deposit & rent for the humans & pets. Our pet deposit is nonrefundable because we anticipate dogs & cats will do some degree of damage.
Clearly stating applicant criteria will save you a lot of time & headache. Be proactive & upfront in communicating your expectations to the residents. Lastly, if you have a good relationship the neighbors of the property, ask them to let you know of any suspicious activity on the property.