Keep the crankset, just remove the unnecessary rings (need stack bolts to re-assemble).
At least keep the front brake for now. Keep the tires, just rotate the front to the back.

You might be happier in the long run by having a dedicated fixed wheel built for you, it's more
money out-of-pocket, but a longer-term investment than a bum-bike set up.

I converted an '83 Moto Mirage this way for a friend, and it worked out just fine.