i would like your opinions on the best patio cover for the wet season. i need something with a reasonable cost and low maintenance needs.
A roof will be economical and effective.
If the top of your patio cover is flat, you need to build a slope (1/4" per linear ft will do), then cover it with 'flat' roofing materials.
Keep in mind that if you roof your patio, you'll be unable to enjoy the view and benefits of an open patio cover.
Win some, lose some.
Several years ago, I built a 10 X 10 garden pergola. Traditional pergolas would be open and have vines or such on them, but this being Portland, Oregon, I wanted a little protection from the rain and also some shade from the hot summer sun. I chose to use corrugated plastic milk glass panels. The several panels from Suntuf only cost about $200.