Non Refundable Pet Fees vs. Pet Rent

[Amber Forkey]

Looking for some guidance on how to navigate the pet fee world. 

I'll be using petscreening.com and am trying to figure out if I should be doing a nonrefundable pet fee at move in PLUS the monthly pet rent or should I be waiving the pet fee and stick to the monthly fee? In NY there aren't any restrictions on this as long as the pet fee isn't more than one month's rent. 

I understand I CAN do either one or both but I'm interested in seeing what the consensus is with other landlords/property mangers. I don't want to come off as if I'm gouging my tenants by trying to collect both but I'm not sure what the "industry standard" is on this. 

Any feedback is very much appreciated!