Wood – the best method for carrying a 4×8 by yourself over tough terrain

A craft knife or box cutter will do the job very quickly and cheaply. You only need to score the front side of the drywall and then it should snap cleanly enough along the score line.

If you already have a Dremel or Roto-Zip, you can get drywall bits for them that will make short work of any drywall.

Use a hard, inexpensive local wood, without large pores. Hard, since they will get banged around. Pores will allow the wood to trap bacteria, dirt where you don't want it.

Maple is my first choice. Second choice might be birch, sycamore, or alder, if you have a source for them. Poplar is not bad either - cheap, reasonably tough. Cherry would work too. Much depends on what you can find locally. Do NOT go to your local big box store (Home Depot, etc.) to buy hardwood. Hardwood bought there will be quite expensive for what you get.

Woods that I would NOT use are imported exotic woods. These can often cause allergic reactions. Another wood to be avoided for this purpose is walnut, which might cause reactions in some.

Use wood coloring, rather than paint. Paint can chip off, and may not be food safe. And be careful with stains, since many of them will not be food safe. Wood dyes, like aniline dyes, may also be something I would not put in my child's mouth. For a coloring, I would use simple food coloring.