This is a basic problem, and very common.
Your Ruger came with a loose "sporting" chamber. It's looser so that more rounds will feed properly. You can have the chamber recut, and cut your groups down dramatically. Or you can buy an aftermarket barrel with a "bentz" or other tighter chamber. Green Mountain makes great barrels, many for less than $100 (including a fluted .920" x 16" model with a bentz chamber).
The wrong ammunition is only part of the problem.
As far as the ammo goes, I've found most "standard velocity" amunition to be the most accurate, no matter what barrel with what chamber I've shot it from.
Edited to add:
I am considering getting a 10/22 target in stainless with the 20" bull barrel.
First off, 20" barrel just adds more weight. Most rimfire rounds, especially the way more accurate std. velocity, stop gaining speed after 16" or so of barrel.
Second, I'm pretty sure the factory heavy barrels come with the same crappy chamber, which would explain why they aren't that much more accurate than the skinny barreled guns.
The "target" models do come with nice trigger parts already installed, and a nice wooden stock that will accomodate the heavier barrels. I would buy the Target model, then sell the barrel on a site like this one. Then replace it with a quality aftermarket barrel. The install couldn't be simpler, it's just two screws that hold the barrel on. Just make sure to drop in a $8 extractor, to aid extraction from the tighter chamber....