Simple is the name of the game, at this stage. Build the Single Speed with what you can find for cheap. Same applies to a Fixed Gear. Then ride and enjoy the bicycle. One note, do nothing that can't be undone, at this stage.

If you like the ride quality and intend to go Full Monty, do so by researching and collecting components. Sooner or later, you will be able to restore the bicycle. And, for what it is worth, I have been doing this (get the bike road worthy and safe to ride, then ride it) for years. I keep my eyes open for what I need to find and that, for me, is part of the fun of vintage bicycle restoration - the hunt never ends, even though the bike is good to go.