i am feeling nice today:
the old road bike probably came with 27" wheels but most today use whats called 700c.
If you are just doing single speed, go to your local bike store and see if they have an older road wheelset and get them to remove the cassette and put on a bmx freewheel. thats your best and cheapest option.
and yes people ride single speed with a coaster brake but you have to build a wheelset specifically for that.