RE: If you want to get rid of that gamey tast...
I never worry about getting rid of the gamey taste because my deer never have it. There is a simple way to prevent it. IMMEDIATELY after the kill get the guts out and get it cooled down. 100% of the problems with taste come from improper care by not getting it cooled down as soon as possible.
I think the question of processing immediately or allowing the deer to hang is irrelevant. If you get that deer's temperature down below 40 degress as fast as you can it can hang for a while. On the other hand none of my deer have hung more than a day or two depending on how soon I can get it processed. I've even had deer go from on the hoof to paper-wrapped packages in less than 4 hours and it all tastes great.
When you pull those packages out of the freezer don't let them set on the counter all day either, get them out a couple days in advance and let them sit in the fridge or go from freezer to microwave to cooking immediately.
Last but not least whatever you do don't overcook it. I consider venison overcooked if it doesn't have some pink in the middle unless I'm using a moist cooking method. Before my wife met me she wouldn't touch a piece of meat if it wasn't completely well-done, now she won't let me live it down if I don't leave it just a little rare.
TJ