You might look into powder coating the frames since you're thinking a paint shop anyway. Way more durable and usually very handsome.
Vendors on eBay handle lots of Chinese parts for cruisers and other older bikes. Some of the parts can be of decent quality, but others can be disappointing. I've rebuilt a few oldies, and one of my favorite eBay vendors is Abaxo in West Point, NY and Texas. They carry decent quality parts at great prices and are reliable about filling orders. Everything from the frame up there. Your best friend will be a decent set of calipers for measuring parts to assure fit.
There was lotsa chrome on those Chicago Schwinns, it's surprising how chrome polish will bring that stuff back to elegant. Replacing that with new Chinese chrome will not be an upgrade in quality...quite the opposite! Buff and wax the old chrome and it'll last WAY longer than new low quality new chrome.
Sounds like a fun project