Does what I have described sound like a good plan? Can you think of
anything I could change that would make the shelf easier to make, or
less expensive? Thank you in advance for any help.

Purpose of "shelf"? What kind of load do you expect, and what dimensions?
Sounds more like you're building a bench...

I'd build the basic frame on a flat floor to make sure the frame ends up being flat. Don't use drywall screws, they're brittle and will snap under load.
Consider bracing the lower portion of the legs to prevent the legs from shifting/weakening under load. Or just use concrete block as another post suggested.