Don't over light the room.
Our Game Room has LOW Lighting. We have several Antique Lights with low LED light bulbs. One main light mounted in the ceiling 14', then a antique floor stand light in a corner, and another desk light. It is easy on the eyes and you can sit and enjoy the room and displays.
You can put some LED Spot lights to highlight some of your mounts. You have a good size room so plan out how you are going to display. The main thing is the furniture and how you and your guests are going to enjoy the room. We did a Display room with antiques associated with animals, a MAN/Woman Cave, and an Office. We put a extremely nice wood/leather desk, Hand carved wood Italian chairs, couch along with marble top tables. Then of course all animal mounts and antique firearms, knives, ammo. Another thing is don't over load your room. You have plenty of room with 26' x 22'. Our room is overloaded and have to display in other rooms., our whole Family is also a "Hunting Game Theme".
Good luck with setting up your "Trophy/Game" ROOM and getting the correct lighting.