I need to determine if new mattresses require a box spring or if I can set the new mattress directly on the frame I make.

All the 'bed in a box' I've seen don't require a box spring.

Where I bought mine, they included a 'free' metal frame to set the mattress on. It's just a basic frame with fold up legs for easy moving. The only thing I don't like about this frame is that there is no provisions to mount a headboard. Your wall is your headboard.

I've though about looking at a conventional bed frame and the possibility of setting this metal frame inside of it.

Here's a link to the frame I am using >> mattress frame linky

Maybe this will give you some ideas?