Long gun - Yes, you can purchase long guns as long as the firearm is not illegal (no brainer), you are eligible to posses firearms in your state of residence and as long as you get a proceed from NICS.
If I remember correctly, as an out of state resident, you would not be able to purchase a receiver while in Washington.
"RCW 9.41.124
Purchasing by nonresidents.
Residents of a state other than Washington may purchase rifles and shotguns in Washington: PROVIDED, That such residents conform to the applicable provisions of the federal Gun Control Act of 1968, Title IV, Pub. L. 90-351 as administered by the United States secretary of the treasury: AND PROVIDED FURTHER, That such residents are eligible to purchase or possess such weapons in Washington and in the state in which such persons reside: AND PROVIDED FURTHER, That such residents are subject to the procedures and background checks required by this chapter."
Title 18, Section 922 - B (3)
(b) It shall be unlawful for any licensed importer, licensed manufacturer, licensed dealer, or licensed collector to sell or deliver—
(3) any firearm to any person who the licensee knows or has reasonable cause to believe does not reside in (or if the person is a corporation or other business entity, does not maintain a place of business in) the State in which the licensee’s place of business is located, except that this paragraph (A) shall not apply to the sale or delivery of any rifle or shotgun to a resident of a State other than a State in which the licensee’s place of business is located if the transferee meets in person with the transferor to accomplish the transfer, and the sale, delivery, and receipt fully comply with the legal conditions of sale in both such States (and any licensed manufacturer, importer or dealer shall be presumed, for purposes of this subparagraph, in the absence of evidence to the contrary, to have had actual knowledge of the State laws and published ordinances of both States), and (B) shall not apply to the loan or rental of a firearm to any person for temporary use for lawful sporting purposes;