Showers Pass gets almost entirely positive reviews from people that have their stuff. At the high-end Gore-Tex fabrics and eVent will keep you dry while claiming to be breathable.

I have a jacket made of eVent that is made by a british company called Rab. The jacket is the Drillium. It is very waterproof and it breathes well, but I wouldn't wear it for biking in temperatures over 60 F unless there was a deluge. It doesn't have any vents, so maybe a jacket made of eVent with armpit vents and other venting strategies would be more tolerable in warmer temperatures.

I recommend a cycling cap by itself or under your helmet to help keep the rain out of your eyes. That usually works well for me.