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You can freeze the burger meat right away. A double-wrapping with squares of white butcher and you are good to go. Don't forget to label each pack, as soon as it's wrapped, or you'll be defrosting "mystery meat" for the next year, and you won't know if you've got a tenderloin or stewmeat on your hands until it's thawed. I know someone who spaced-out on that important little detail once.
Also, if you don't have much experience cutting up an animal, don't forget about the tenderloins, which are little strips that run under the spine between the hips and the ribs. The back straps, which run on the top of the spine between the shoulder and the hips, are the best steaks. The neck is all sinew, and should be made into burger or stew meat, which you can cook slow and low until it's tender. I normally take the rear legs and cut all that meat into stewmeat, because I love stew and chili and venison curry, and, in my opinion, the only cuts that are really good enough for steak are the backstraps and tenderloins.
(As a side note, I'll just add: I do my own cut-and-wrap on a couple of deer every year and a couple of lambs. All the advice everyone gave above, about pulling the hide off, not covering it with a tarp, etc., is really good advice. Also, you did the gutting yourself? That's the hard part. The rest of it is just the simple process of taking big pieces of meat and turning them into smaller pieces of meat.)
(edited to add a couple details.)