Square tube or C-channel for gate frame
Square tube (or I-beam) is a trifle stronger than C-channel/C-beam. You may not need that additional strength, depending on exactly what you're building. C-channel is a bit lighter, which may not matter for your application.

(I'm using square-tube aluminum for the bike trailer I'm modifying. C-channel would probably have been fine for this application, but the weight and price differences were insignificant so I went for overkill.)