Well, I hate to be the bearer of bad news, but you will not find a rod that is suitable for everything from stream trout to king salmon.
If you plan on targeting the kings then a 10' 9wt. If you latch into a hot coho or fresh king, be prepared for a long tiresome fight if you go much lighter. I have watched cohos on the Oak explode $600 fly rods, they will make your life miserable if you are not prepared to catch them. I learned my lesson my first trip up there trying to fish with a 10' 7wt, it just didn't have the stones to do anything with those salmon. With the extreme crowds, a 20 minute fight is not going to make you any friends.
However, if you are going a little later in the season when most of the salmon are zombies, a 10' 7wt would be perfect medicine to handle the steel, browns, and the occassional moldy salmon.
For a compromise a 10' 8wt might be what you want. Its gonna be a little too light for the fresh salmon and a bit too much for the steel/browns.
I wouldn't consider any of these rods very suitable for stream trout fishing. However, if you would go any lighter than the rods I mentioned, you are likely to have some major issues with landing fish (in a timely manner) on the oak.