I have the bed of my 49 F1 totally torn down, tomorrow the rear crossmember for the bed frame should be here along with all the rivets.

How do I go about setting the rivets?
My thoughts are I'll install them and put a small spot weld on the backside.

What is the proper way?

 

The easiest and best way to set rivets properly I have found to be using an air inpact gun with a rivet setting bit in it. I purchased my bit from Jim Dix at Big Flats Rivet in (I think) Horseheads NY. I just got a sale flyer from HF that had an impact gun with several different sized bits. After inserting the rivet in the sheet metal, cut the protruding rivet shank length to approximately 1 1/2 times the rivet shank diameter (to properly form the head). Make a bucking bar out to a chunk of metal (need some weight). I dimple a crater in the bucking bar to be held firmly against the rivet head. Note that it is easier to do with a helper on the bucking bar. Then heat the extended shank of the rivet to cherry, push the tool firmly against the shank end of the rivet and a quick burst from the air impact will form a perfect head.
Last winter I did a major re-rivet job on a frame replacing 110 rivets!