I've had chickens for 17 years (not the same ones!). They take up very little time and the children would benefit - they love to collect the eggs! Four is a good number.
Feed is quite cheap, I buy a sack of layers' pellets which lasts about 6 weeks and costs £6.75, and a sack of mixed corn which lasts twice as long (ie you only feed half as much to the chickens).
I only clean mine out properly when they really need it, in between I "poop-pick" - that's just collecting the poop that has gone in the nest box or in the middle of the floor. I put seed trays under where they roost at night so I can just whip them out and empty as required. Even a full clean only takes half an hour or so.
Chickens will lay most days when they are young, and hybrids do lay throughout the winter - pure breeds not so much. As they get older they lay less eggs.
You have to be prepared for some losses - Mr. Fox has called twice, causing major carnage, and sometimes hens just die for no apparent reason. Also you have to arrange a chicken-sitter if you go away.
I find chickens very rewarding, it's great to watch them scratching around (mine free-range) but they can dig up your plants in their search for worms and bugs. Their used bedding makes great compost when added to the heap. Go for it - it's (nearly) all good!