BigR-
I hunt in the Okanogan area (north-central WA), and while there are grizzlies in the area, you would have to look long and hard to find one. Many black bears, though. If you are planning on going to the northeast corner of the state (Pend Oreille Nat'l Forest), bear spray might be a fair precaution, but in general, I would not worry about it too much.
Western WA has wet, rainy weather during most of the hunting seasons, but is spectacular in every way, especially on the Olympic Peninsula and along the Columbia River Gorge. Elk hunting and blacktail deer in both those areas, but not an easy hunt. Southern WA has the Columbia River as mentioned, but also has some steep, tough country around Mt Adams and Mt St Helens (yes, the one that blew up). Eastern WA is drier and more remote, with rolling hills and prairie. Northern WA is mostly volcanic and short-grass prairie (desert, to many folks), but has very good deer numbers, both mule deer and whitetail deer.
As for guns to bring, most folks here hunt with bolt action rifles, lots of 270s. 308s, 30-06s, 7mmRemMags, 300 WinMags, and 338 WinMags. And 2 7X57s (that I know of
).
All in all, WA is a good state for hunting, but not great. There are lots of hunting opportunities, but many areas have been hunted pretty hard and animals are pretty wise. Bird hunting is fair, except goose hunting which is very good. Varmint hunting is getting better thanks to the bunnyhuggers getting trapping banned. So come on out and bring your guns.