yeah you are going to need a new rear wheel to accommodate the cassette. I'm pretty sure you'll be able to stretch the drop outs out.

Are you trying to go index or friction? How much of a beater is this going to be? Is price a factor?
If locking it up and not worrying about is a priority, I almost think you should find the cheapest wheelset that you can find that already has tires/tubes and a freewheel, get a rear derailleur, chain, and the cheapest friction shifter you can find.
Since your frame doesn't have downtube braze-ons, you will either need some sort of stop clamp or a clamp on downtube shifter or you can just run cable housing all the way from shifter to rear derailleur.