All (or almost all) of the quality gun safes out now are fireproof. A burglary safe that is not fireproof (like would be found in a jewelry store) would be much more expensive.
I did quite a bit of research into safes earlier this year and decided on a Cannon. It had a higher fire rating than others I looked at and came with an electronic lock which I find to be -much- better than a dial combination lock. This type of lock is an option on most other safes but is standard on the Cannon.
Yes, you have to be concerned with moisture but, as others have noted, a Dri-Rod or Goldenrod will take care of most of that for you. It's not really a pain and the only extra effort required is running an electical cord through the back of the safe. I also have a large can of dessicant on the top shelf of mine for extra insurance but I doubt it's needed.
One last thing, be sure to look at what size you need now and double it.....at least. You know how collections can grow and a fire safe is also a great place to store those important papers, the wife's jewelry, all kinds of stuff you want to keep safe. This is not a purchase you want to have make again in a year or two.
A good safe in a good size is not cheap by any means but it should be a once in a lifetime purchase that will protect it's contents well.
Joe/Ga