I find Goretex worthless on a bike and just use cheap coated nylon. I wind up soaked either way. I seldom if ever use my rain pants on the bike, but guess I would if it were cold enough (the coldest it was when we were in the rain on that tour was the upper 40's or maybe 50F).
I used small stuffable rain jacket and pants from Sierra Designs on my Trans America. They came with a little stuff sack. They were cheap and non breathable and worked out fine. They were not bike specific. BTW the jacket did not have a hood and I did not bother with a helmet cover or rain hat, but again if it were cold, maybe... The pants were only used in camp.
Bike cover? I never bother, if it is in the rain all day what difference does throwing a cover over it at night make? Just lube and generally maintain the bike while touring and don't worry about it getting rained on while on tour.