On my list of 19,674 things to do, "build trellis for side of garage before March" is on the top 20. My requirements may or may not point to a certain kind of wood:
1) No treated lumber
2) No preservatives (applied by me) allowed, unless it's a food-safe substance
3) Don't care if it rots in one or two or five years - I'll make another.
4) Don't care what color it weathers to. A clematis plant will completely cover it anyway.
5) 8 feet high
Cedar? Redwood? Other suggestions?