We can our beef in large mouth quart cans. An All American pressure canner is used. A bit of the meat is cubed, but by far most of it is ground. Most of it is browned first, not all of it. Large mouth cans are a lot easier to reach in and wash the jars. Small mouth can be used, but you will need a brush and hot water to clean them, and it will still be harder to get them clean. With the large mouth jars, a child's hand or a small adult hand can fit in and clean them properly and easily.
We can beef, pork, and venison the same way, perhaps grinding some beef tallow or pork fat in with the venison if we have some available. The most common thing we use with the venison is ground bacon ends. It is inexpensive and has a good flavor.