Backstrap is the best cut of venison because it is the most tender. When I have it ,which is very rare, we'll butterfly into cutlets and fry them in a cast iron skillet after they have been dredged....think chicken fried steak. Of course you'll need to make gravy from the grease to put on top.
All of the above are excellent. If it was a young doe, I like to slice them about an inch thick. Wrap them in bacon like a filet mignon and cook them over indirect heat and smoke until they are just crossing the threshold from medium rare to medium (about 150ºF). Just a little fresh ground pepper for seasoning.
Cut it into filets and pan fry with salt & pepper. While the filets are resting after cooking, pour a little cognac and cream in the pan, and whisk the sauce for a minute or two. Add a little fresh black pepper to the sauce and drizzle over the filets (on the side is fine too).