My 0.02:
Many factors come into play, but meat prep starts even before a shot is taken:
SHOT SELECTION:
Acquiring a nice rack while getting premium meat is unlikely from the same animal - especialy without "aging" the meat. A young, non-stressed, corn-fed doe probably offers the best tasting meat if you can't dry- or wet-age the carcass.
Razor sharp broadheads and shot placement are paramount so that the deer expires quickly before the acids build up in the muscles from running. Recover the deer as soon as you can.
GUTTING/SKINNING:
For those of you that learn best from visual aids (like me), this gutting video is helpful:
http://youtube.com/watch?v=ECdaKBbmGnU (though I've never seen a milk-sac cut!) The deboning video featuring these two guys is also very good; I'll try to find it.
With a lung-shot deer, you could raise the head uphill and use the blood to flush the lower parts (out the pelvis) instead of using water.
Be extremely careful about not touching any of the scent glands while gutting/skinning, or getting ANY intestinal contents/fluids on the meat (including hitting only vital organs - not guts). If you do, wash those parts well, or discard them.
Remove the inside-loin chops ASAP, and bag them, as they are the best meat, and will dry out quickly.
Skin off will help in cooling, but also causes some drying if hung. Fat on will cause gamey flavour, but definetely helps with retaining moisture if hung. Unless you're hanging, remove any bits of fat (gamey taste - especially in rutting bucks).
Hanging a carcass head-up at first will drain blood the best, since most of your gutting-cuts are near the rear-half of the deer anyway. Then hanging the carcass head-down will let gravity aid in skinning and deboning.
AGING:
John McCreary, that's a great idea to age meat in an old fridge.
There's no question that aging meat will tenderize it. It basically starts the process of tissue break-down... i.e. early stages of rotting to put it bluntly. Dry-aging refers to hanging a carcass open to air in a clean environment with a stable temperature of ~1 degree to 7* Celsius. Length of time varies according to who you ask: generally 2-7 days, but up to 28 days. Wet-aging refers to vacuum-storing the cuts of meat in refridgeration before freezing.
GRILLING:
Last year I converted my sister-in-law from a venison-hater to one who is addicted; she keeps asking me when I'm going to bring her some more to grill. As far as the recipe side, since venison is so low in fat compared to beef, I prefer to marinate it in simply oil & vinegar.(you can even add marinade before you freeze the meat in zip-loc bags, so the meat will marinate as it thaws). My favorite is - after marinating - to make a rub/paste of butter/oil + whatever your favorite spices are. Montreal Steak Spice added liberally to a rub and massaged lightly into the meat will make almost ANY meat taste great. Almost as good is to just olive-oil it before grilling with spices.
Remember, meat will continue to cook for a few minutes even after you remove it from the grill, so if you're not sure if you should take it off... it's probably ready. I use the "poke" test - simply poking the meat on the grill with my finger to see how much "give" it has. The more firm, the more cooked it is.