Thanks for your reply.
I'm flexible on the design at this point, but am a relative novice at this. I was thinking of basic cabinet construction (plywood case with face-frame). It will be a display case, so about 6 ft high and about 18" wide with an enclosed (doored) section on the bottom and open shelving on top.
Ok, so cabinet doesn't exist yet. One common method is to incorporate legs into corner posts of design. Bottom 6" (or whatever) is tapered, rest is basically 2x2 that acts as corner. This eliminates attachment issues as legs are now integral part of design and not add on.
If it were me I'd make legs from 2x2's and use them the fullheight of cabinet. Make cross bars at top of bottom of display space. You can rabbet or dado the sides of the legs to receive glass or panel (back). Gives simple, strong cabinet. Attach cross bars with Mortise & Tenon (hard) or biscuits (easier).
Run rabbets/dado full length of leg, Taper two inside faces of leg. If you use dado on cross members inside lip of horizontal can act as bottom shelf support. Run dado on center of top horizontals for top insert. Rabbet used when there is possibility of having to replace panel (ie glass sides, front), dado used when panel will not have to ever change (solid panel for back, top, bottom)
This design is very plain. You can dress it up with a small piece of molding inside frame. Miter at corners it will look like rail & stile but without the difficulties.