cmbmw, you could get a Simmons Aetec from Wally World for $100, and a target barrel for that 10/22...the combination of those 2 things will do a lot for both target shooting and plinking. I've got an Aetec 3.8x12, and it's a lot of scope for the money...it would be perfect for what you have in mind. I've got it on an AR now, with a set of ARMS #22 high rings, fwiw.
Several companies make drop in, factory channel target barrels. Green Mountain has 2 at least.
I'm sure the Leupold is a fine scope...but it's almost twice what you paid for the rifle, and isn't really gonna help it shoot any better.
A stock 10/22 is not gonna be a tackdriver, and you probably aren't gonna be using match ammo...so you're gonna have an accuracy issue that the best glass in the world isn't gonna solve.
Between a new barrel, and a hammer replacement, you're group size will drop in half, I can pretty much guarantee it. After you've done that, then look at scopes.
BTW, I have a 36x BSA on my 10/22 lol...I like to be REAL sure of the bullseye [:D] But I wouldn't hesitate to put that Aetec on a your 10/22.