Congratulations on your first blood. I'm glad you won't have much in common with the hunters where you grew up. Respect and gratitude are critical and keep you healthy.
Re: meat generally, but game specifically, especially lovely delicate cuts like tongue:
CONSIDER A SOUS-VIDE SETUP. Investment up front might run you $50-100, maybe another $20 if (like me) you detest the idea of cooking in single-use plastic and would rather grab an easily-washed silicone set you can reuse indefinitely. The wattage is next to nothing, unlike the slow oven-braising methods most people use when they aren't sure how tender their critter will be; it doesn't heat up the house in the summer; you can get precisely the appropriate level of doneness and sear it quick on a hot pan or with a torch. Leftovers? Reheat them to exactly the right temperature, with zero effort. If using silicone bags they wash absurdly easily. It also makes EVERY PORTION not just edible, but an utter delight: shank? Neck? TENDON? Throw it in with some spices and let it go for 24 hours, then pour that liquified collagen goodness over some rice. With butter & fried herbs. (The water bath setup will also be useful for lots of other things, too, from bottle-warming for infants to yogurt-making to pasteurization of eggs.)
Butchering your own is pretty much the only mustachian solution unless you have an outright disability, IMO. It reinforces gratitude & connects you to the source of your food take it from field to table, it's VASTLY less costly, it's a useful physical and intellectual skill to develop, and it's excellent traditional human labor, best enjoyed while talking with family or friends. You can create whatever cuts you like, you can package it in portions based on what your household consumes in a given cooking timeframe, if you want extra jerky you just make extra jerky - and because time is money for a professional processor and they aren't going to delicately trim the last bits of backstrap from the spine for you, you're more likely to do the work to get more meat from your animal, which is both ethical and economical.
The "gamey" taste people fear comes from two things: hormones, specifically testosterone (e.g. most the beef you've ever eaten comes from steers), and careless processing: letting meat sit too long, too warm, get dirty, etc. (Remember the "respect keeps you healthy" bit I said earlier?) Technically there are some diet exceptions, especially with omnivorous or predatory animals - I generally don't eat anything with feet that eats other things with feet - but really it's those two: age & sex, and a quick transition from the hoof to the coldbox.