Welcome to the area... The river pages on this website are one of the best resources around for river info. They are community driven, so anyone who is a member of this board can contribute beta to the river pages and we strive to have them updated often. The American Whitewater river pages (which I'd assume your're familiar with) are really good. Besides that, although its nearly 2 decades old, Jeff Bennet's Guide To Whitewater Rivers of Washington is a book every paddler should have. It's been out of print for some time but used copies can be found online. Hopefully Jeff will think about updating it again one of these days.
I can give you a few general guides for rainy season boating:
• West side boating. It's mainly the rivers on the west side of the Cascades that run during the rainy season, which basically starts in October ususally and goes until snowmelt starts. The east side rivers just don't get enough rain in the fall/winter and have most of their precip locked up as snow.
• Fall boating is great, but FLASHY. From Sept to November, when it rains the water runs down the mountains fast. Its ususally falling all as rain (not snow) and the ground is often hard still from summer and water just runs off fast. So when it rains look for rivers to rise fast and drop fast. Oddly enough paddlers come down with a lot of 1 day flus this time of year.
• Winter boating is a bit more reliable. By late November, ususally the ground is more saturated and water leeches out more slowly. Also, more of the precip is falling as snow and just having a snowpack slows down the rise and fall.
• Also, dig deeper into the info available on rivers you're interested in. Lots of info and clues are out there for those who look. Also, be aware that although this website has current flows for rivers, some of the gauges, depending on what agency the data is pulled from do not always update on the main pages here. It pays to click on the links to the actual pages for the gauges to see what's really happening there.