You've received a lot of good info here... great thread!
I wouldn't think of dropping my game at a butcher for the following reasons:
>cost (reasonable, but I don't hire things out that I can do)
>control (portion, cut, etc.)
>responsibility (if it's screwed up, I know who and how)
>chain of custody (much of the reason I hunt is to know where my food comes from; if I drop it off, I don't know for sure)
>quality (I know EXACTLY where cuts came from)
>bragging rights/respect, especially for non-hunting friends and family
You don't need to invest in a bunch of stuff, although we all know you will, eventually. I do over 90% of my cutting now with a butcher knife (Google S112-8PCP). I have over $1,000 in nice German and Japanese cutlery, but this is my go-to butcher tool. A good boning knife does the other 10% (Wustof in my house, but Dexter-Russel S131F-5PCP would fit the bill just fine). Finally, the best piece of butchering equipment you can buy is a honing steel (not for sharpening!). Use it every half hour or so to keep your blade wicked-sharp. If the blade is dulled, you'll have to resharpen with something else. Do not ignore the steel.
I don't grind much meat (~20 lbs, tops, from an elk), but investing in a decent meat grinder is worth it. $120 or so should get you there. More importantly than burger (for me), this allows you to make delicious sausage from scratch (and not from lips and azzholes). Mmmmmmm.....sausage.
I waited for several years before buying a grinder, though, and ate just fine. Instead of grinding meat, I cubed tough cuts and used them in stew, chili, curry, cochinita pibil, pulled elk, etc. Plan on slow, moist cooking. I have elk chili on the stove right now, and I expect to cook the meat for 5 hours before it is fall-apart tender. In my not-so-humble opinion, whole-meat stews and chilis knock the socks off those made with ground meat.
As noted previously, clean everything well. Cool your critter quickly and keep him/her that way throughout the process. This is your food, treat it as such. We tape butcher paper over the whole kitchen bar counter to stage meat, and cut on a large wood cutting board. Do not suffer hair on your meat. Everything that goes into the freezer should be fit to feed to company. Work on one quarter at a time, and have bowls/bins ready to divide cuts. Label each meat pile/bin as you cut. Enlist a friend or family member to pack while you cut. Label packages with date, species, specific cut (e.g., "2012 deer loin steak"). Freeze packages flat, and preferably in single layers so that it freezes fast. Do not overload your freezer and expect good results.
I vacuum seal everything now, and if my sealer broke tomorrow, I'd buy another. The difference in meat quality (especially after a couple months) over Ziplocks or freezer paper is shocking.
On to the meat:
Everything from the front shoulders is tough. Stew. Grind. Pot roast (this is the home of beef cuts like the 7-bone roast and chuck; excellent flavor, but not designed for steaks). Same goes for the neck and ribs. Briskets and flanks on elk are worth cutting and saving separately. Deer? Grind/stew/leave.
Backstraps/loins are for steaks. Cut thick (1 1/2"). Tenderloins are for tender, buttery steaks and seducing women. If you've done a sloppy job of field dressing, or have a less-than perfect shot, you may have to leave the tenderloins in the animal. This is regrettable.
For hind quarters, refer to this excellent diagram from RMEF:
http://www.rmef.org/TheHunt/After/Carnivore%E2%80%99sKitchen/Recipes/WildGame101.aspx. "Tougher Cuts" should be cut into jerky (across the grain), cured into corned deer/elk (this is fantastic, BTW), ground, or stewed. "Tender Cuts" should be steaked or left as roasts (medium or medium rare, please). I tape a printout of the diagram on the cabinet while I'm cutting, mostly because I'm usually exhausted and a bit punchy by the time I'm 6 hours into cutting.
We eat heart and liver fresh. For some reason, I am reluctant to thaw and eat liver. Cut liver thickly, soak in several changes of water, then whole milk. Dredge in flour seasoned with salt and pepper, cook to medium, serve with caramelized onions, eat with rich red wine and roasted potatoes.
Lastly, if you like to cook (or plan to like cooking), you should make stock from your trimmed bones (save some for Fido, too, obviously). I pressure can stock into quart jars or pint jars, but you can also fill Ziplock freezer bags with stock and freeze them. I put up at least 21 quarts (three canners) of stock every fall. It goes into every batch of stew, chili, pot roast, gravy, etc. that I make. My basic stock includes five pounds or so of bones (I like neck, scapula, front legs), two onions, a couple carrots, five stalks of celery, three garlic cloves, ~10 peppercorns, ~5 whole cloves, 2 bay leaves, a small fist full of thyme sprigs, and about 8 quarts of water. Roast bones and veggies first if you want a dark, roasted flavor. Raw ingredients into water produces much milder stock. Simmer for at least 4 hours, preferably more.
Remember to have fun while cutting food for the year!
Eli