Then I vote for C-channel as the flanges won't protrude anywhere near as much as the leg of an angle iron, whether equal or unequal leg lengths. According to my steel book, a 2" x 1/2" x 1/8" Bar Size C-channel has a flange width of 1/2". Weight is approximately 1.43 pounds/foot. The 2" x 1/4" flat weighs in at 1.70 pounds/foot.
Even though the stress may always be pulling as you say in a perfect world; the reality of the situation is that C-channel will be less likely to buckle than flat bar will. If you have a vertical bandsaw, you could always rip some C-channel from 2" x 2" x 1/4" square tubing, which will make for a stout brace.