There should still be books about kites in the hobbies and crafts section of a decent town library... Even a "Golden Book of Kites" has examples of these:
A simple, cheap and dependable flier is the Scott Sled - a trash bag, three sticks, some tape is all. Fies in light winds, and practically upwind of where you are on the ground. Not very dramatic or maneuverable, and not too good in strong winds, but it can go a long way straight up in the right conditions.
For a bit more maneuverability, delta kites do nicely. Two leading edges and a cross strip to keep the swept wings spread. Bridled on a keel of the same (usually plastic) as the wings. These should still be available in "department stores." Hint: steering them is backwards - you want it to bank to fly left? Move the line to the right... Want it to climb? Pull down on the line... Makes sense if you think about it, but it just seems backwards. I wonder how many dime store delta kites were busted because the instinct was to pull it in the direction you wanted it to go...
The "standard" two-stick kite doesn't need a tail, if the bridle is located right, and it does better if it is LIGHT. Choppy winds make it more sensitive to bridle location, and make a rag-tail helpful. The knots were probably to get the weight without an excess length of cloth ...
And if you really want to go far out... Squadron (I think it was) made airplane-looking kites - Sopwith Camel, Fokker Triplane, possibly a Spirit of St Louis. Even sillier? They sold a kite in the form of a square rigged sailing ship! These flew! Really!
Many years ago, I decided that since it got windy every time I went out to fly ukie, I'd bring along a kite. Might as well, right? So, we got a lot of rain, weekends, those years... We ukies are potential techno-nerds, right? I wound up using the bottom segment of a deep-sea fishing rod, with an old deep-sea reel. The 3' extension made 'steering' a kite easier. The reel held several hundred feet of 15# monofil, and I got near the end of that many times... With a rolled up Sled hooked to the rod and reel, all it took was to shake it out to make sure the bridle wasn't fouled, lift it above your wind shadow and pay out the line. ...Up and away!
A thought: A Scott Sled in moderate breezes, *"safely near" our flying circles, can give a visible "profile" of the wind at different heights. It is amazing the changes in direction and speed that a kite line can show you. (* - "Safely near" -downwind, of course, and probably about as far away as a good portion of the height the kite reaches.) Unless the wind changes V drastically, a kite like this can sit up there hour after hour...
All basic Sled and two-stick kites are simple to make, and the kids will enjoy them more when they've made them. The deltas are probably better bought ARF.