Zinc is a good metal for a kid to use for casting. It's easily available at a scrap metal dealer (at least it used to be) for next to nothing. It melts at a low enough temperature that you can melt it on the stove, with effort, or with a propane torch. And it's quite non-toxic, certainly far less toxic than lead. (I have a special page about zinc safety that addresses in detail the question of whether casting zinc metal is a health hazard.)
Arguably tin is the best metal for amateur casting, but it's much more expensive and not generally available as scrap metal unless you live in a large city with exotic scrap dealers. In any case, growing up I never had access to tin, but I had plenty of zinc.
Lost wax casting is about as ancient a technology as they come. The first step is to make something out of wax. Any kind will do, but note that paraffin isn't wax, and you can't work it other than to carve it. Beeswax is better, and you should be able to get it at craft stores (candle making section). (I got my supply at an apothecary in Zurich and took it to America in a cloth suitcase. When I picked up the suitcase after the flight, the outside was smeared with a thick layer of greasy-waxy stuff, which of course I assumed must be my wax melted out so as to cause a horror when I went through customs. Turns out my wax was fine, it was just some kind of airplane slime that had gotten on the suitcase.)
Anyway, after you've finished your wax object, you attach a conical stem also made of wax, then pour a mold-making compound around the whole thing, leaving just the end of the wax cone sticking out. There are many proper ways of doing this, and many proper mold compounds. I, of course, didn't have any, so I used plaster of paris to make the molds. It's cheap and can be found in any hardware store (in the drywall supplies section).
I would make a cardboard box about 2-3 inches larger on all sides than the wax object, and open on the top. Then I would drip hot wax onto the bottom and stick the top of the wax cone onto it, leaving the object standing up as if it were a wax flower on a wax stem. Next I would stick long pins or needles through the cardboard and into the wax object at several locations (the places that would become high-points inside the mold when it was turned right side up for casting). The pins helped hold the wax object in place, and when removed the holes prevented air pockets when the metal was poured in.
I would mix up the plaster of paris to a slurry consistency, then pour it into the box. I learned after a while that it was very important to work out air bubbles. Since then I've seen films showing special vibrating machines designed to do exactly this, but I did it by shaking, and by reaching in and swishing my fingers around the object to brush off any bubbles that might be clinging to it.
After the plaster hardened, I would remove the cardboard (which was all soggy), then bake the mold over a tray of aluminum foil to remove the wax.
It takes a very, very long time to bake a mold, all day for a big one. And I definitely learned not to cut corners on the baking time. You've got to make sure all the wax out, and that the plaster has had all its residual water driven out of it. If you try this, you'll probably ruin a few before you believe me on this.
If the mold isn't completely baked, the metal will sputter and bubble when you pour it in, often shooting balls of still-molten metal flying. The only time I've ever burned myself working with metal (or gunpowder) was when a drop like that landed on my hand. After that I wore gloves every time. And of course this ruins the mold too. (It goes without saying that you must be wearing safety glasses any time you pour molten metal into a mold. Just try to imagine how painful it would be if even a tiny bit of molten metal seared itself into your eyeball.)
Most metals shrink when they harden, which will result in voids in cast object. (There are several methods for avoiding this, but they involve spinning the mold at high speed in a kind of centrifuge. That strikes me as dangerous.) I tried to minimize the problem by letting the mold cool after baking (but not overnight, as it would then absorb moisture again), and then playing a propane torch over the top of the cone of molten metal right after pouring it in. My theory was that this would make the metal harden from the bottom up, drawing in more liquid from the cone as necessary. I'm not sure it had much effect.
Once the metal was solid, I would start dribbling water over the top of the mold, to hasten the cooling process. This was dangerous, because if any liquid metal had remained, it could have triggered a steam explosion. But I was of course impatient to see what I'd made! Hot baked plaster of paris is amazingly porous: You can pour a steady stream of water onto it and the water will vanish before it's even spread much over the surface, as if you're pouring it straight into the solid material.
When the metal was well solidified and the water had stopped hissing, I would take a hammer and bash away at the plaster until it cracked open revealing the metal object inside. It took a good bit of cleaning with a screwdriver and wire brush to get all the plaster off. And of course I always had to cut and file off the filling stem, along with any bumps caused by bubbles, and the little whiskers from the needle holes.
I'm not saying this is the best way to do lost wax casting: It isn't. It's just the way I did it.
Other good metals for casting include lead which is very easy to melt and easy to get at hardware stores, but is toxic enough to worry about especially if you file or sand it. Because of the potential for permanent brain damage, children should never cast lead themselves. It's not so much that the vapors are toxic as that kids can't be expected to rigorously wash their hands after touching the lead or anything that has come in contact with it.
Copper and its alloys brass and bronze are of course the classic casting metals of antiquity, along with silver. Copper is easy to get from scraps and cutoffs of electrical wire, and it's not poisonous. Silver is much more expensive, but not as bad as you might think. $50 will buy enough silver rounds from a coin shop to make several nice objects. Unfortunately the melting points of copper and silver are high enough that you have to use something hotter than a stove top to melt it. A charcoal fire with a blower would do, or a plumbers torch with MAPP gas (for very small amounts). An electric crucible is ideal, but expensive. There's also a recently discovered technique for casting metals with a microwave oven. Ask your mom first.
The other really good metals for casting are tin and aluminum. I've never had enough tin cheap enough to do much with, so I can't tell you any specifics. It's probably a lot like lead. Aluminum melts higher than zinc, tin, and lead, but not nearly as high as copper. An electric kiln or propane torch will work. Aluminum is really easy, you can get it from cans, broken window frames, old pots, whatever. But here's a word from the wise (David Ried, not me): You'll get much better casting results if you melt down old things that were themselves cast, rather than extruded aluminum. Cast aluminum contains silicon which greatly enhances the ability of the molten metal to conform to details in the mold.