Removing membranes and silverskin before freezing is important, IMO.
This ^^^^^
I've been doing my own since I was a kid. I've paid to have a few done but only if its warm and I don't have time to do it. As Bighorn posted, I remove everything that isn't meat. Deer fat is horrible. Remove all the fat, connecting tissue, and 'silverskin' and you'll end up with lean meat. For the burger, you'll need to add some fat to get it to stick together when making deer burgers. I normally use pork fat mixed with my burger. The last few years, I've been turning alot of the burger into sausage. As daividlea pointed out, it don't suck with biscuits.
Vacuum sealing is also the way to go. We used to wrap meat in freezer bags but it doesn't last long enough if you shoot 2-3 a year. I've always liked cutting up whatever I kill. It is an extension of the hunt.
