[Arran]

The Philco 625 is from the 1936 model year, and it's actually a decent radio even though it isn't a top end model. It has six tubes, three bands, with a tuned RF amplifier stage, the 37-33F while the cabinet looks similar, is a single band battery operated radio. This is actually a lot better of a set then I was expecting, I'm not 100% certain of this but I think the veneer in the front panel may be real. What's more it still has good original grille cloth. Unlike a battery radio it's more practical to restore and actually use as a radio.
I think the suggestion of using an old sideboard, or some similar cabinet, maybe a good idea. One thing that people used to do around here was buy wardrobes that a local auctioneer would import from Wales and Scotland, build some shelving on the inside, and use it to house their TVs and other electronics equipment. A wardrobe is kind of big for your purposes but you get the idea, but there are all kinds of cabinets, shelves, and even steamer trunks that could be retrofitted with minimal effort.
Regards
Arran