I do both. I do most of my game myself. I figured it out over a couple decades of cutting up my own deer. Now I’m doing my own elk and caribou. I usually kill one whitetail each year, keep the backstraps and tenderloins. Then I take the quarters to a game processor for jalapeño and cheddar sausage. I have my own electric grinder because my family mostly eats ground meat (burgers, tacos). Then I keep large roast pieces for crockpot roasts. That’s honestly my favorite way to eat my game. My wife has several great roast recipes.
I second the Victronox knives. They are cheap off Amazon, cut well, and sharpen easy. I do a double layer freezer paper wrap, only because I don’t have a vacuum sealer (I really should get one).
For your first deer or two- I’d recommend taking it to a processor. You should be able to find a processor that will take quarters in game bags (I’ve had good luck with the Caribou brand bags). Over time you can learn how to break them down yourself. For me the most enjoyable part is doing everything from the shot to the table. It’s important to remind ourselves and especially our children that meat doesn’t come wrapped in plastic from the meat isle at the grocery store.