For $100 I also suggest the Marmot Precip. I had once for a long time but was never super happy with the fit of it for my build. (Nothing from Marmot fits me the way I'd like)
Looking at Patigonia.com it looks like you can get last year's colors of the Torrentshell for $90. Very similar jacket and their fit is better (for me anyway)
2nd hand is a great option. We have a consignment store in town that specializes in outdoor gear. I ended up selling my precip jacket for like $40 to someone at a gear swap. It was like new.
Personally I'm back to a 3-ply Goretex shell. Little heavier, much more expensive, far more durable options available. This is after having a high end Patagonia H2NO jacket delaminate under very little actual use.
Finally I don't think you'll find anything comfortable during a hot AZ rain shower. There is really no such thing as a highly breathable waterproof coat. The finest goretex jacket is still going to make you sweat terribly if it's 80° and your moving, even in the rain.