Well, you can photograph wildlife in your back yard or a local park, but you can also backpack far into the back country and sleep overnight in a tent. So, the requirements for equipment can be very different depending on the locations you plan to frequent.
Since you stated equipment other than lenses and camera, I'm assuming you have thought that part through.
Here are just a couple of ideas that haven't been mentioned that I'll toss out.
I really like carrying my gear in a photo backpack. I usually have two bodies with me, one with a 500mm and the other with a 100-400 zoom. The backpack makes it easy to carry two setups, which is my preference. Even with one camera, a backpack to carry a windbreaker, a lens or two, lens cleaning kit, extra batteries and memory cards, etc. is nice. If you go the backpack route, I advise spending a little xtra for a comfortable, adaptable and photography specific backpack.
Since I have lightweight gear, I don't use a tripod often. When I do, though, I'm glad I spent a little more for a reasonably solid tripod.
Don't underestimate the value of having more than one or two batteries or memory cards.
I try to remember to bring an old plastic bag with me. It's good to sit on if the ground is wet, and I also try to carry some trash out with me if I can.
A comfortable hat that won't easily bow off in the wind is pretty essential, IMO.
That's just a few things off the top of my head. Hope it helps a bit
ENJOY your time shooting wildlife!