damp (not wet) paper towel rub down to get any blood that has not been gotten out of the cavity. then a dry one to finish up.
It should look like a carc [no swearing please] hanging in an butcher shop.
Skin and bone as quickly as possible to release heat and prevent spoilage. Try to get the deer down to "primal cuts" asap. If you're hunting bigger game (elk,etc.) this is even more important due to the size of the cuts, and the amount of heat the hide and bones can retain.
The meat will harden over at the surface, protecting the meat inside. ("glazing over")
If in doubt, mixing a bit of veg. oil and chili oil and spraying on with a spritz bottle will deter yellowjackets, etc. Rubbing black pepper on the meat is also good for this, but remember you're putting the pepper on your hand, your hand on the meat, your hand BACK into the pepper, etc.--that can contaminate the pepper or leave YOUR bacteria on the meat. Shaking the ground black pepper from a can is prob. best.
as far as the taste on reaheating--there is "NO" fat on a deer...and the meat does get stringy and gamey the 2nd time you cook it. Its breaking down in the cooking process.