I use 3 layer Goretex- made by Goretex but it does not pack down and is expensive.
There are plenty of "Cheap" rainjackets out there that will keep the rain out but they do not breath. I went to an outdoor shop that caters for mountain and serious outdoor pursuits and bought a water proof top by Karrimor. Waterproof and vents to keep me cool without letting water in. And folds up small enough to put in a pocket. Look to similar shops for similar products. They have more experience in outdoor clothing but it will not be bike specific.
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How long was I in the army? Five foot seven.
Spike Milligan