Kidproof, you can get away with any of the Stackon security cabinets, assuming you mean "kid" kid and not "juvenile delinquent" kid. I have the 18 gun model I believe, got it from my dad when I headed to college, and I've seen it hold as many as 10-12, and if someone stuffed it with care and had socks over their guns, it could probably push 16. It's not electronic though, it's a key which most security cabinets will be, which will be a huge pain if you lose your entire keyring with a week to go before hunting season. Ask me how I know.
Looking at Academy a second time, I do see among proper safes the Cannon Safari 14 gun with electronic mentioned earlier, as well as the Liberty Safe Revolution 18, Winchester Bandit 9, and the Stackon 10, all of which are mechanical combination locks. Among security cabinets, they have a very shallow Stackon 8 and a Stackon 18 similar to mine, both keyed entry. All of those are under your budget.
[This message has been edited by ajn142 (edited 9/8/2013 9:42p).]