Nice one! In my experience any BB of that standard would fit, just make sure to put enough spacers under the sprocket to set it off the frame. Of course if we talk durability, try to get sealed 90's BMX set, but if looks is what you are after you may as well just clean up, grease and restore some old 2nd hand ball bearing set.
For the headset you have less options, since there are not so many different 1" 32,5mm headsets out there nowadays. Most probably you'd get an older model one or have to customize it yourself. There are options of getting a NOS or reissue Schwinn headset if you are going to convert to threaded, but for the thread-less option you'd be looking into older BMX bikes again.