I'd say if you get to about 2" at 50 yards for 10-shots, reliably, from your stock 10/22, you're doing pretty well. I refuse to feed mine stuff that I know will really, really shoot, mostly because it's a $200 plinker, not a $2000 match rifle. I've noticed the difference in accuracy between CCI Green Tag and CCI Mini-Mags to be around .5" or so out of my 10/22. I'll stick with the Mini-Mags for half the price.
Ammo, I've tried CCI Mini-Mags (both 40gr solid and 36gr hollow point), Green Tag. Rem/Eley Target Rifle, RWS Target Rifle, Win Supreme (horrible in this rifle), T22, Super-X 37gr HP, 40gr Dyna-Point, Federal AutoMatch bulk (good in original lots, had a couple of bad ones and haven't bought any again in a year or so), CCI Blazer 40gr solid, Remington Golden Bullets 36gr HP (surprisingly accurate in this and my Single-Six), Federal Bulk pack 36gr HPs (varied from excellent to so bad I was wondering if I forgot how to shoot), Federal 510, CCI Stingers (worse than the worst packs of bulk ammo!) and I'm sure others I've forgotten. The one constant: My average groups at 50 yards rarely seem to go much better than the 2" range. Maybe a little under, maybe just over, but hovering right around 2".
That said, I think things like a better stock, trigger and sights would make a world of difference. To me, the standard carbine stock is too short and chunky. A Hogue or stock from a Deluxe Sporter (DSP) would be an improvement. Add either a scope or a set of aperture sights and a trigger job, and you'll probably have increased accuracy and usability.
Actually, a Hogue or DSP stock and a Williams receiver sight are on my to-do list. Maybe after a Marlin 39A or a 77/22 though!