Go to the discount department store and look at the rod and reel combos. Kids will have the easiest time with a spinning reel with a trigger release. Dads will love the open-face spinning design for untangling line.
Take the kids with you when shopping. The premise is for them to pick out their own, but really you need to make sure that their fingers are long enough and strong enough to pull the trigger.
My five-year-old has had a Quantum Snapshot 10 combo for two years now. It cost about $20 brand new, and there's nothing wrong with it; I've used it for hours at a time.
We looked at some inexpensive one-hand ultralight rod and reel combos. The smaller and lighter reel would have been great, but the triggers were too hard to pull.
Fact is, even the cheapest junk can catch fish:
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