The chair seat is 14 inches from the ground, so it fits perfect. (Chair is KidKraft, found online for cheaper than we could have made it for. Plus, a chair would have been harder than a table!)
After building the table, I primed it, did two coats of Behr "490c-3 Balmy Seas" semi-gloss paint (it took very little paint), and then three coats of Minwax Polycryclic in clear semi-gloss. It may have been fine with just the paint, but the polyurethane gives it a really durable, wipe-able surface that is perfect for a kids table.