For the sides, just cut one side out, clean up any jigsaw mistakes with sandpaper or a plane, then use that as your template for the other side. Unless you plan on making a few more side panels for other machines, i wouldn't bother making a stand alone template. If you do decide to make a template, use thicker plywood. 1/4" warps a lot and it's not a lot of material to run a bearing on, especially since you're a routing rookie.
side laminate - that'll work
CP - Use a forstner bit if you can for the button holes. The result will be much smoother and more accurate.
cp box - there's no need to miter. You're just going to get aggravated if you don't have quality tools. Just change up your design so you don't need to. If you're going to cover the box, you'll never even see the mitered corner. Just do a lap joint or if you've got the routing bug, do a rabbet joint.