What's the best (minimalist) way to cook venison, specifically the backstrap?
You can cut it into medallions or leave it whole. This is a very lean piece of meat. You can handle it as a steak and fry it in a skillet. However the middle should be (medium) rare, whatever your steak preference is. I would advice against a slow cooker method, but I haven't tried it.

After frying it in the skillet, use the sticky bits to make a wonderful sauce (with some red wine).