OldIHC

The truck has copper single flange 3/8 tube brake lines.
Do I want to stay with copper, use steel or stainless steel? Does double flange pipe need double flange fittings?

Copper is not a good Idea, do not think it is legal anymore to use. Here is what I found on a search in the forums: search.php?keywords=copper+brake+lines&terms=all&author=&sc=1&sf=all&sr=posts&sk=t&sd=d&st=0&ch=300&t=0&submit=Search

Steel or a hybrid might be a good choice. Just remember to double flare the ends.

If the truck has air brakes, then copper is ok, most fittings were compression type, but you could flare.
Until the advent of nylon air brake line, everything used copper for the stationary lines and rubber where it had to move.
The main draw back to copper is cost and the fact it work hardens over time. You can remove and anneal it or just replace.
Copper is not used on hyd brakes.

It is air over hydraulic. Both the air and hydraulic have copper. I don't mind changing materials. I want whatever is best. Steel probably is cheaper.