It all depends on what leagues you have available. If there's silhouette shooting in your area, you are well equipped to do that. You can probably do some form of action shooting (police style). With the 22 you could shoot bullseye. But again, gun games aren't much fun unless you have a league to play in. Preferably one that doesn't require a road trip to participate in. Keep an open mind. The best way to find out is to call some gun shops and ranges.
Colfax isn't far from Lewiston and they have a great silhouette range there. They could also tell you if there is anything in Washington closer to you. I know at our Idaho State Matches we usually have a good turnout from Spokane. In Lewiston they shoot NRA small bore, Hunter bore, and Cowboy Rifle, both small bore and pistol cartridge. I don't have any names for you but maybe someone from up there will read this and post some more info.
You might want to check to see if any of your local clubs sponser any small bore bowling pin shoots. They are a lot of fun and relatively inexpensive. The big bore classes are fun also. They're geared for fun and generally award prizes to all classes of shooters. My whole family used to shoot pins. My wife and my boys when they were 12 and 14. With 4 of us sharing firearms it was a nightmare for the one scheduling the groups. We'd run 4 to 5 shooters at a time. 5 pins and 6 bullets, 8 rounds starting with 10 seconds and working down to 3 seconds. Winner was chosed by total pin count.
IPSC can be a lot of fun too. It's a lot more structured than pins. Sometimes you can run into a Master Class shooter with way more attitude than he deserves but mostly it's a good time.
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