To support them I normally use one of two techniques
Either make a rack to stack them on out of scrap wood with long drywall screws or brads driven through the rack so you can set the part on the points of the screws, normally on the rabbets on boards, or the parts that are covered in mounting.
Doing it that way you have three (or four) tiny little pinhead spots that should be invisible when you're done, and if you're concerned with them you can hit each spot with an artists brush when everything else is done.
Other method is to drill small holes on 'invisible' sides and stick brads in the holes, then tie string to them and hang them from the rafters so they hang visible side up.
My coaming boards have two small holes in them where I used wood screws to hang them.
If you have screw holes etc, use those holes to hang the part.
Normally I have as many scraps of plywood with screws driven through them as I have parts to
varnish.
For me old brushes seem to work best, new brushes always seem to have loose bristles they shed in your nice new
varnish. And I just can't seem to get a decent finish with foam brushes.
Good varnish, and good brushes combined with carefull prep is the key.
Ken.