Taking your questions from the top:
If you want to build this out of solid pine, you'll have to get glued-up panels, because you surely won't find any 20" wide pine boards! I know Home Depot carries them, but I'm not sure whether they have panels > 16". This may actually be a good choice for you if you're working in a condo, with limited space to maneuver 4x8 sheets of plywood. Of course, you could also have the lumber yard cut do the major cuts on your plywood for you, though you can't expect them to be more accurate than +/- 1/8".
Plywood is uniform, stable, and easy to work. And, depending on your source, you can get it in many hardwood veneers. I like to work in red oak and maple, myself, though I'll use birch if I'm painting something (also will use MDF if it's to be painted).
With plywood, for the edge, you can by plywood edge moulding specifically designed for the purpose. Or, you can get "iron-on" veneer tape in the same specie as your plywood, which is what I always do.
For furniture work you want a good carbide blade like Freud. My main blade for finish work is a 50-tooth blade. For plywood I have an 80-tooth blade. Be aware of whether the top or bottom of the board being cut will have the cleaner edge. For hardwood veneer plywood, even an 80-tooth blade is apt to tear oak veneer. You can put masking tape right down your intended cut line to minimize the problem. I also have a steel plywood blade that also does a fine job.
Hope this helps!