The military understands that civil aircraft may need to use their fields in an emergency. If it's 121, the extent of your paperwork will probably just be the same IOR you would submit for any diversion and the company will handle any follow-up. It would probably take a while to coordinate PAX handling and transport, although if the base has a military pax terminal that would simplify things.
The fact that you're 121 means they won't be to concerned about who you are or why you had to land there. If you're not 121, you'll probably be answering more questions as security might be a concern.
Hostility and suspicion might be expected from the quick-response security forces (that's their job) but the duty officer should be easy to deal with. This assumes an actual emergency...if you landed their by mistake (it happens) I know of cases where they've refused to grant a take-off clearance, which means you have to hire a mechanic and a truck to disassemble and remove the aircraft.
You'll know you're in real trouble if they call the FBI..the military can't detain or prosecute a civilian so they need the FBI if they think there are grounds for that.