What type of humidity is good for a game room to best preserve my mounts? I assume dry? Is there such thing as too dry? Occasionally I run a dehumidifier in the room when it is very humid outside.

"To" dry may be harder on your mounts than a bit humid. Think of them as leather as "dry" can be very harmful.
Keeping them out of direct sunlight is also a must, not only due to the heat, but the sun light will fade the colors.
Your prized trophy hanging over an active fireplace is also not recommended.

good point! didnt think of them as leather but guess I should have well maybe I will not run the dehumidifier so much then afterall