As someone looking for a place this summer, who also has pets, I think most of us in this situation are willing to pay an extra deposit or extra money a month, but probably not both, unless it's very reasonable. Personally speaking, my pets are family. I've paid an extra $50 a month for my furry kids, and have paid an extra deposit.
Fencing is always appreciated, as is sturdy flooring. I used to be in charge of the rental division of a real estate company for several years, and carpet is almost always a bad idea. A lot of the homes I rented were pet friendly, and I got to the point where I would put in the lease agreement renters would be responsible for flea bombing ( or something along those lines) before move out inspection, and if not, renter would forfeit part ( or all ) of the additional deposit. There were some owners who wanted part of the pet deposit as non refundable, regardless.
I'm happy to help in any way I can.