For the stated level of security, the invisible hinges and a solid door with a deadbolt should be fine. You might line the interior with plywood, but if a thief is willing to trash your house, or worse, has a sawzall, then you are out of luck anyway unless you have a real safe. I don't think you'll need the touch latch, you can open the door with the key in the deadbolt.
You will want to rest the gun butts on something softer than the recoil pads but firm enough not to bottom out over years of storage. My local hardware store had some closed cell foam that was perfect. It also had some wood moulding that had a long series of bumps that's perfect for rifle rests.