Luminous, with children in the house I absolutely recommend getting the firearms locked away. A safe with a digital code would be optimal, but not necessarily the best.
The safe can also double up as your safety deposit box. I use mine for everything that is important (i.e. cash, documents, harddrives, jewelry, etc). Once you have a safe you'll find yourself using it for more than just firearms and ammo, especially with the better safes which provide a certain amount of fire protection too.
Kids are curious. We can't fault them for that. Educate them about firearms safety and answer their questions truthfully. You want your children to come to YOU for answers when they have questions about guns. You do NOT want them getting those answers from their friends, cousins, uncles, etc.
Basically, once you've tamed their curiosity about guns and once you've taken away the mystery surrounding them they will be less likely to "experiment" with them, thereby reducing any risk for accidents.