If it were me, and I wanted a single speed, I'd get an 80's 10-12 speed in decent shape for $25-$40, remove the un-needed parts, and put a bmx freewheel on it. Thats about it.

Your $25 frame doesn't seem like a god deal.

BTW I broke a Miyata 714 aluminum frame where it's aluminum tubes GLUE to the lugs at the bottom bracket, while standing up pounding up a hill.