Dunno where you are in the Valley, but here's my run-down....
I don't know much about the North side. It appears from your suggestion that Avery is your first choice. I've never been there, so I can't comment.
I've been to the Phoenix Rod and Gun Club at South Mountain a couple of times. Their facilities seem somewhat limited, IMO, but depending on where you're coming from, it may be OK.
I'm a member at Rio Salado. They have a fairly large facility (but not as large as Avery), and a fairly diverse list of programs. I shoot IDPA there most months, but they also have IPSC meets at least once a week. Lots of long gun shooting available too. Their one drawback is a very limited facility for shotguns.
And speaking of such, if you're a shottie-lover, check out Red Mountain Trap and Skeet. I'm not much interested in this, but it is available.
Indoor Ranges. [Important in the summer
] I wouldn't waste my time at Shooters World. They used to be great, but have declined significantly (although, in fairness, I haven't been there recently.) . I've never been to Scottsdale Gun Club. Their website appears to show a nice facility, but I'm guessing it's pricey. I got my CCW and renewals at Caswells in Mesa. For me, it's close to home, and they had a good program (In my uneducated opinion.).
Gunshows are about every other month. I like Crossroads of the West shows best.
Links:
Caswells
Scottsdale Gun Club
Shooters World
Phoenix Rod and Gun Club
Rio Salado Sportsmans Club
Red Mountain Trap and Skeet
Oh yeah. Welcome. You'll love it here.
AZLib.
Resident for 18 years and counting