Patience and perseverance should find you a decent older road bike for $200 or less. Add a rear wheel like you said you're done. Or you can go uber cheap and just get a cog and BB lock-ring with some lock-tight, redish/respace and run a "suicide wheel" with the existing wheel (no skidding though!) You could then sell the un-used components to re-coup a bit assuming they're decent pieces which would hint at a decent bike to begin with. Prices quoted above are certainly not top shelf stuff at all. I'd look for and older frame with no shifter bosses and the like. Look for tubing material rather than specific brand, such as Renolds, Columbus, Tange, ect. There should be a sticker on the seat tube designating what it's made of. Good luck and happy wrenching/riding.

PS a job would still help