Well, I've left this thread alone for a time and now I'll weigh in. When my eldest son was 3, (he's now close enough to call it 21), he was always pestering me about my guns and wanting to "help" me with them. For his 3rd birthday, I took him shooting. Among the guns he got to personally pull the trigger on were the following: .22 rifle, .25 auto pistol, .380 auto pistol, .45 ACP auto, and an AR-15.
He got to see what each round would do to an "action" target, ie, can of soup or beans, tomato, watermelon, etc. I had initially thought that the noise and recoil would intimidate him to the point he'd e a little less likely to want to do that, along with my explanations of what the results would be of a bullet striking a human as opposed to a soup can or watermelon. He was suitably impressed, but not exactly what I had in mind.
He learned that guns, while fun and exciting, can also kill with no remorse. From that day forward, he never bother to mess with any of my guns unless he asked to go shooting and I was with him. Oh, yeah, at age 3 he was not quite capable of handling by himself any of the above mentioned firearms, so I was holding them and letting him pull the triggers. Let me be very clear here, at NO time was my 3 year old holding a firearm all on his own.
Once I took him shooting that first time, in a controlled and safe environment, and let "him" shoot Dad's guns, he was fine with them. The curiosity factor had been dealt with, safety issues drilled into his little head, and I never had a problem after that. Now, he can pretty much out shoot me with any firearm you want to hand him. He knew every part of an AR-15, how to disassemble and reassemble, and properly maintain by age 7. Today, I'd not hesitate to say he's a self-taught gunsmith and can and will astound you at a gunshow.
Point here? TEACH your children about guns and gun safety. That act itself will do far more than all the locks and safes ever will. Not all parents are as gun safety aware as some of us are. If you don't resolve that innate and natural "curiosity" in a controlled and safe environment, you risk them doing their own discoveries in a manner that you wouldn't be proud to tell the world about.
That being said, lock up your guns if you will to keep the kids away, but I'd much rather your kid have access to it and KNOW how to use it just in case he/she ever needs to to defend themselves or even you. As for a cheap safe, Wal Mart or try checking out the IWANNA or maybe Craig's list.