I use a poncho set I got from walmart, just cheap pvc. Jacket and pants, doesn't breathe for crap but keeps the rain out and keeps me warm (if not hot). I need to tape over the "pocket" flaps, as they let some water in. I've managed to get plastic grocery bags, tied as high as possible up the leg, and the pantlegs zipped overtop the bag, to work fairly well, but not had any serious time testing that, it was a one-time event that lasted maybe 15 minutes, maybe ten or so miles at most.
I NEVER use my rear brake unless I'm holding on a hill. I've had it slide on me, when I went through a three-foot puddle in a parking lot doing like maybe fifteen miles an hour. I didn't realize I had any pressure on the pedal, and have since made darned sure to NEVER have my right foot on anything other than the ball, unless I'm holding on a hill. I'd much rather have to get a little harder on my fronts and engine-brake the rear. When the weight shifts to the front, the rear is easier to lock up and cause a controllable situation to go bad fast.
Waterproof footwear helps with keeping the toes dry as well.
If you've had one time being cut off, consider yourself lucky... there for a while it was a weekly / bi-weekly occurence.
When it rains, the very start is the worst, as the road slicks from all the oil and such that collects. After the rain has been falling for a bit, it'll wash off, but til then be ubercareful. I usually ride in the left-hand position within the lane. Center is to be avoided in inclement weather, as cars do drip oil and other slickery substances.
I've never had problems with my windscreen (because it's so small that I can only see through it if I'm literally laying on my tank, and even then it's optically distorted... danged 250). My visor does bubble up, but like in a car I only have trouble if I"m being hi-beamed or in orange street lights. I've noticed that the water beads off quickly if I turn my head to one side or another.