Design advice? Laundry folding table

[Dave Richards]

I would be inclined to use a cleat on the wall behind the machines and metal legs with leveling feet at the front corners. Like this. You can add some stiffeners underneath the top. They can be glued so no screw holes from above. The top would be screwed to the cleat on the wall but the screws can be covered with a piece of trim. I've used carpet tape to stick down bits of trim when I wanted it removable with no visible fasteners.

Edit to add, you could also skip having anything running to the floor and make brackets to support the table top. Or you can buy metal ones. A cleat on the side of the brackets in my sketch would allow you to attach them to the top with screws from below.

I think I'd prefer the first option because it would allow easier access to the backs of the machines without having to pull them out all the way.