I've been around a lot of yard sales and flea markets and have seen plenty of good solid bikes that looked terrible, tires flat and rotting, dust caked on the paint etc. Most were built in the sixties and seventies in the USA and could be had for $5 bucks. The main thing was they were build in a time that they built quality bicycles that could actually be worked on, overhauled, maintained and expected to last a few decads.
If you buy one of these, expect to take a few days to pull it down and clean it to where it looks like new. Check the rims to see if they look true by turning the frame upside down and slowly rotating the rim to see if there are places that seem bent. If they look OK, then just check you spoke tightness (1/8 turn each to start with if they seem loose) You'll likely buy new tires, tubes, and rim bands for your project.
Different bike makers use various construction techniques. I paid $5 bucks for a Ross which has lugged frame tubes. (these are fancy looking fittings the tube is inserted into before the brazing or welding takes place) Some use butt welds, while others make special extrusions for the frame head where the forks mount, the pedal crankcase, etc. These have nipples that the tubing is
inserted over before the welding takes place and afterwise is ground smooth
so it looks seamless. (Schwinn used to do this)
If you go to a public library or the net and look up bike frames in bicycling books there will be chapters which address all this. But for not I'd suggest
that an older bike for cheap that doesn't appear all rusty may be a stable platform. Often boy grow up leaving the bikes behind in the garage, basement, or barn and that's it until mom and dad want to clean the place up.
Many a good bike is had this way for purposes like yours Finfan.
In recent years some cheap crap has been made and sold thru volume discount stores. I've talked to bike mechanics in old time bicycle shops and they have shown me some examples of this. In a book we were assigned to read in Design School, titled "Design for the Real World" by Victor Papanek....the surveys listed various items and their life cycles in the USA compared to other countries. A bike in the USA would last 2 years where in like India it would last 50. (from good care) But I figure places like India wouldn't have the cheap junk sold or purchased there by big discount chains.
So, read up on bike frames and what's "quality" and hit some yard sales. I once purchased a Raleigh made with special Reynolds tubing at a Goodwill thrift store for $15 bucks (that had sold new for over $700) Often yard sale, flea market, or thrift store people haven't a clue what the stuff is worth.