My folks grind in pork shoulder with their venison, and I haven't hunted in a while, that said I'd keep the venison ground by itself. You can always add ground pork or beef or veal or lamb at the point of cooking.
We process our own critters and did when we had our fram. We make a lot of deer burger and sausage each year....like as much as 200 pounds most years and sometimes more.
Prior to deer season I hit my local livestock processor and place an initial order for beef and pork fat-usually 5-10 pounds of each. The fat gets cut into 3/4-1" cubes, frozen on sheet pans and then vacuum packed, When making burger or sausage we take out what we need and re-seal the bags. If what we're making would normally be from beef we use beef fat and likewise for pork fat.
Most burger and sausage waits until after the season so we can see what we have to work with. We pack the meat in 12# bags (see below for that size reason...) so I order the bulk of the year's fat after the season when the butchers aren't hoarding it for deer season.
Our family prefers the juicier mouth feel of deer burger with 15-20% beef fat. Most commercial sausage is 30-35% fat but we like 20% so 3# of fat for 12# of lean fills the 15# stuffer just fine (usually with a bit left over due to the bit of added water).
If the burger was ground without enough fat you can add fat anytime. Just cube the fat around 3/4", freeze it to what meat processors call the "frost crust" stage (not fully frozen) and toss it in a food processor and pulse to the desired size. Be sure to gently fold it into the ground meat. As ground meat has a lot of exposed protein every bit of handling you do will tend to make it bind up more and be less tender. FWIW, most folks like the visual appeal and mouth feel of fat particles that are a bit larger than the lean particles. When grinding I generally grind the lean and fat separately then fold them together prior to bagging or making sausage.
We're a half hour north of Winston-Salem. If anyone wants to get together sometime to grind meat, make sausage, make corned venison or beef or beef/deer pastrami etc let me know . I've done a bunch of presentations for sportsman's shows and helped teach some game processing seminars when we lived in NY.
You can also add a bit of bacon grease or wrap the burger in a strip of bacon to add a bit of flavor. I don't condone using ground pork simply because I eat my deer really rare and rare pork isn't on my menu.
I typically buy steak trimmings when I grind my deer for burger, that has worked well for me over the years.
When grinding sausage I've had good luck with boston butts and deer mixed 50/50 for patty sausage and 60/40 deer/pork mixture for smoked link sausage.
I process my own and just stop at the local butcher for beef fat. They usually have it on the side or can order it quick and only charge like a $1 a pound. I grind mine 4 pounds meat to 1 pound fat. When I make the burger just some garlic powder and season salt thrown in. If you make sausage just ask the butcher for pig fat. I like that better than pig shoulder because there is less pork mixed in.
Beef fat from a butcher ground in with the venison is my go to. I've used beef suet before if I couldn't find any regular beef fat but I could tell the difference from the regular beef fat. Another recent one I've tried is running a 1/4 lb of chopped bacon to 3lbs already ground venison, and ran them both through the grinder again. That's my new favorite. Bacon is a bit more readily available as well.
For burgers I really like the A1 Sweet Mesquite dry rub. Not mixed in to the burgers but coated liberally on the outside of the patty. Topped with a slice of pepper jack.... Burgers so good make you wanna slap yo momma!
Hey, Eric! i just noticed your comment on bacon fat. A little bacon drippings added to ground beef or venison (especially if it's really lean) can really punch up the flavor and mouth feel of a burger or meat loaf. And a 1/4 cup added to the oil for a pan of homemade French fries (or even chicken fried or country fried steak) really perks them up too.
I keep a coffee can of bacon drippings in the kitchen fridge freezer for stuff like this.....