The word venison is used loosely when it comes to cooking. All of these recipes work great for any antlered game that you are planning on eating. With that being said, not all antlered game meat is created equal and have their own nuances.
I wouldn't be shocked if brawls were started during debates over whitetail and antelope meat quality between Western and South Eastern hunters. The best way to make the decision on your favorite is to try all of them out for yourself. Many of my friends trade different animal proteins throughout the year, which is a great thing to do if your hunting range is limited.
If you're trying a meat from an animal that you haven't tried yet, it's best to first choose a recipe that lets that ingredient shine and by that I mean a simple recipe. The fewer the ingredients, the more you will taste your prized gold that you worked so hard for.
Below are links to various venison recipes that are categorized by the cut of meat or cooking technique.
Backstraps and tenderloins are best cooked as steaks or roasted whole, rested to a temperature of no more than medium (145 degrees Fahrenheit) and then sliced across the grain to whatever thickness that you like. With that being said their versatility doesn't end there. These cut are naturally tender because of their lack of connective tissue can make a good chicken fried steak, carne asada or stir fry, but you have to be willing to part with your thick cut steaks. And if you cook the meat too long it can become a bit livery tasting.
Deer meat from the back legs benefit from the same cooking techniques as stated above for the backstraps and tenderloins but with a few more options. Here you have the choice of cooking an entire leg (minus the shank) bone-in or boneless. You can cut the leg crosswise into bone-in steaks, separate the muscle groups at the seams for smaller sized boneless roasts or cut them down even further for boneless steaks.
Cooking with these parts of a deer is where the benefits of low and slow moist cooking come into play. Think stewing, braising, plus a combination of braising and smoking. The lower temperatures and longer cooking times break down the connective tissue which is mainly made up of collagen, turning the meat into succulent tender eats. The broken down collagen also naturally gives body to the cooking liquid, which in turn makes soups, stews and sauces even more delicious.
You also have the option of grinding the meat from these cuts for burger and various sausages. Just make sure that you remove the silver-skin and any connective tissue that you can to avoid clogging up your grinder.
Ahh yes, venison offal, the odd bits, peasant fare. These are the parts of the animal that most hunters usually throw out. When prepared properly, they can be some of the tastiest parts of a deer. They do require a little bit more work in the kitchen due to their delicate nature, but I think that work is well worth it considering an animal gave its life in order to feed us. The tongues are great braised, hearts grilled, liver prepared a multitude of ways and the kidneys seared in clarified butter (my favorite way).