In the field:
I do all my field dressing and/or boning meat out in the field with a Havalon. They're amazingly light and God's gift to the backpacker and mobile hunting community in my opinion.
At home:
1) A good boning knife. I researched options a few years ago and ended up with two; both Victorinox. One curved blade and one straight. If I could have only one it would probably be the swept but both work great for breaking apart deer, hogs, etc.
2) Grinder. I started with a hand grinder, then a 1/4 hp and have been using a Cabelas 3/4hp for several years. They all work but the bigger grinder makes the process much faster. I haven't used the newer Cabelas carnivore series but the older Cabelas grinder has been excellent.
3) Vacuum sealer. No brainer here.
4) Meat tubs/cutting boards. These items, while not mandatory, I would still consider basic equipment that makes life easier.
The extras:
1) Sausage stuffer. You can use most grinders with attachments but a stand alone stuffer makes the process easier. I usually just make bulk sausage but when you have time, bratwurst or hot dogs can be fun.
2) Dehydrator. Again, not critical that you own one of these but venison jerky is amazing so this is something to consider.
I've processed a lot of big game from hogs to elk. If you have any specific questions feel free to PM me and I'll give you my phone number. Butchering your own game has many benefits and no cons.