Cleaning apartment, previously pet owned

Put on a mask and mop all open surfaces a couple of times. - I just saved you big bucks.

After vacuuming and wiping down all surfaces, steam clean.

It used to be such a nice neighborhood, before the pets started buying all the apartments. Tsk tsk.

Be sure to clean all duct work (if there is any) and replace all the filters on the HVAC/AC/etc units.

I moved into a place in college that was housing a huge dog and the amount of hair that came out of the vent system was ungodly.

If there are wood floors, you could have a problem with cat pee, which permeates wood and is very difficult to remedy. You may need some serious deep-cleaning by pros for that.

Lol yea pet owned.

Good news is the floors are the original ones and need replacing, so that's not a big deal.

I guess I'll do a thorough cleaning of surfaces, steam clean, then change filters. Any other tips?

The filters and ducts are the biggest thing, everything else even if you miss will "wear away" from a few regular cleanings.