Yes, you can call the Sheriff's office first, as SAR teams are all county-based. They will request mutual aid through the state offices if they need additional resources, which then contacts the other counties.
If you call 911 you end up "somewhere in the system" and while they're good, they won't respond nearly as well as calling the SO directly.
The best is to call the rangers, who'll have that information and work closely with the SO offices all the time. If you call the rangers, they'll usually start the process even faster while the ball gets rolling with the SO. If you call SO directly they'll usually loop in the rangers first anyways since they're closer, familiar with the area and can respond more quickly and efficiently. If the rangers call the SO, it'll carry a little more "weight" than random citizen X calling it in, and they'll give the SO better details since they know the area very very well.
Better: Sheriff's Office
Weather, location and situation, though, do make a difference as to how fast and hard everyone responds, as BG points out. Sometimes all it takes is Rangers + SAR dog teams and a general callout isn't required.