Runner or French beans are good and big so easy to see what is going on. If you want to grow them on a balcony maybe choose dwarf varieties. There is a way of starting them in transparent plastic cups so that you put a roll of damp paper towel in there to hold them up against the side of the cup. Then it is easy to watch the different parts develop:
roots, seed leaves, true leaves etc. Once the seed is well sprouted transfer it to a proper pot with
compost. Another way to see how seeds germinate is any sprouting salad such as mung beans in a jar or cress on paper towels. The bonus is that they are ready to eat very quickly which is good to maintain kids' interest.
If I was going to do the runner beans in a cup thing I might also do broad beans as they germinate differently. They sprout from a different place on the seed, and they leave their seed leaves (cotyledons) behind under the ground and only the true leaves come up, unlike the runner types which use their cotyledons for extra photosynthesis and bring them up above ground.
And once you get into botany I would also sprout some wheat so you can show how some plants only have one cotyledon. This year I am growing some hostas from seed and it wasn't until they germinated that I realised they are monocotyledons. They are related to lilies and asparagus.