Welcome!
Where did live previously if you are new to the U.S and Washington?
Since you have no experience with firearms (other than air rifles), you would be best served by seeking out a Hunter Education Course, which will teach you how to safely handle and transport firearms along with other things.
It is also required for everyone born after Jan 1, 1972, before a hunting license can even be purchased. Some info here about the course:
http://wdfw.wa.gov/hunting/huntered/classes/basic.phpOne example of good and bad information you may get from various sources is the clerk telling you that your loaded rifle cannot be transported in your vehicle, this is correct.
However, the clerk saying you could not transport ammo together with the rifle in the trunk is incorrect, provided the rifle is not loaded.
You will find that there are a bunch of very helpful guys and gals on HuntWa, so again, welcome!!