To answer the original question in the thread title, I purchase veneer online from VeneerSupplies.com. Paper-backed veneer is not terribly difficult to work with. With a good contact cement like Better Bond Titan DX (also available at Veneer Supplies) and a scraper, you can achieve very good results without having to vacuum press the veneer, and without having to fuss with the preparation of non-backed veneer. I find the contact cement method much better than PSA-backed veneer, too. I have yet to have a veneer delaminate on me due to a contact cement failure, and the paper back helps keep the cement from bleeding through and messing up whatever stain or finish you put on the wood surface.
As far as price, a 48" x 96" sheet of, say, 10-mil paper backed walnut veneer runs $64.10. A full sheet of 1/4" walnut plywood from an online source I use runs $74.24, and it needs to be cut down to ship. You would probably still need a substrate to put the 1/4" plywood on. A 3/4" MDF core walnut plywood runs $178.24, and still needs to be cut down to have it shipped. I dare say a $64 sheet of veneer bought online, a sheet of 3/4" MDF from Lowe's, and a quart of Titan DX will save $50 a sheet, and I can have the veneer laminated in a couple of hours.
As for the edges, I feel a thin strip of "real" hardwood to match the veneer works quite well.
If you want to test it out, I'd be happy to mail you a few scraps I have laying around the woodshop in the basement. I have walnut and cherry still, I believe. PM me your address and I'll mail you some. You can test it out at home and see if you like the look. You will need to supply your own glue. While I recommend the Titan for your final product, you can test it out with any contact cement from the hardware store.