As others have said, plan for as big as you have room/budget for.
The first two things to do here are determine where you want it to be within your home, and figure out your budget. If you want to go with a vault/room, take a look at American Security vault doors (and keep an eye on Champion, as rumor has it that they're getting into this space as well).
If you want a safe, there is a LOT of good info
here. The long and short of it is that it's easy to get distracted by pretty paint and gee-whiz interior layouts, but (for a home gun safe) there's no substitute for steel in terms of security. In terms of fire protection, I prefer a poured/concrete solution over sheet rock, but either of them is better than a blanket type solution.
As others have said, understand that anyone with enough time and motivation can get into anything... and the name of the game (realistically) is to make it inconvenient enough to get to your goodies that the bad guys say fuck it and go to your neighbor's house. It's kinda shitty to say, but that's the reality of it. Additionally, feasible/realistic security isn't about guarding against what is
possible, but against what is
probable. Is it
possible that a bad guy show up to your house with a 600V generator and a heavy duty plasma cutter? Sure. Is it
probable? Not for most of us.
Again, as others have said, the best approach is to have several layers of security; each layer on its own wouldn't be a showstopper for most burglars, but in combination, it's a really effective approach. Most of us aren't going to be targets of burglars who know how to defeat an alarm system AND intercept/jam a cellular uplink for security cameras AND have safe cracking skills (or the kinds of tools to be able to cut into them). Further, an easy way to avoid becoming a target for burglars is to not have stickers, etc... on your vehicle (no Browning Buckmark stickers, etc...), and keeping a low profile regarding your goodies on the Internet (I'm proud of my toys, too, but I don't post pictures of many of them, and CERTAINLY won't post a picture of the entire collection).
Food for thought.