Guy,
If you get lucky enough to harvest a deer and then they let you gut it couple of things to think about:
If someone's helping you make sure you know where all of their soft parts are out of the line of force of your blade, seen guys get cut bad when something cut a lot easier than their partner thought.
I don't know about y'all but ticks are terrible down here all season, check for ticks after you finish.
I keep a pack of baby wipes so I can wipe down right afterward. I think Wally world sells a "deer cleaning kit" that has some shoulder length plastic gloves in it if you're worried about fluids.
Check for cuts because you can cut yourself in all the fluids and not know it, especially if you have sharp knives.
Hygiene? We've got knives at our club that I know have only been rinsed off from season to season.
The thing about gutting deer is that there are very few heavy cutting tasks, most of the cuts in cleaning a deer are slicing type cuts. I do probably 85% of the cuts with my finger along the top of the blade. A bunch of guys at my club use a small 1 3/4" 3 finger knife that I make. It's more than enough knife for an Alabama whitetail.
Make sure your knives are shaving sharp, it's dangerous to gut an animal with a dull knife.
I'd take my Grandfather's Buck just because it'll be a touchstone between the generations.
Sorry for the long post, but this is why I started making knives (hunting)