I have been bitten by the rimfire bug. I have had a Ruger 10/22 for many years and they are pretty good "plinkers" indeed. I read about more plastic parts on the newer models. Some variability of accuracy is also reported. Something between 1 and 2 MOA is probably the best you should expect, and it will take finding the right ammo for your particular rifle. And occasionally, you will find one that is a MOA or better. As for customization, you can go nuts and easily spend as much as you want on a Ruger 10/22. The most common upgrades would be 1) trigger job and 2) replacement stock, 3) replacement barrel (well, at least the original receiver is still on mine). Hang out on Rimfirecentral.com and you will find tons of info.
As for the cost/accuracy ratio, though, a bolt action CZ-452 American (if you can find one) is the best deal, IMO. The CA-452 American has just been discontinued, though, and is replaced by the CZ-455. I believe that the CZ-452 Varmint (heavy barrel, no open sights) is still readily available new. Many dealers probably still have the CA-452 Americans available, I think, but probably not too much longer. At around $400-500, a CZ-452 with a $20 trigger job will hang with all but the most expensive target rifles.
Other 22's worth considering might be the Henry H001, Marlin 39A or Browning BL22, Grade 1. Those 3 are lever action carbines, and all three will chamber short, long, and long rifle rounds. The Henry is the least expensive, the Marlin the largest with the longest barrel, and the Browning, of course, the highest quality of the three.
The best bang for the buck in any 22LR semi-auto may well be the Marlin Model 60. These have a good reputation for accuracy out of the box and are relatively inexpensive. They have a tubular magazine -- 12 or 13 22LR capacity, I think, vs the standard 10-round rotary magazine on the Ruger 10/22. Ruger 10/22 and Marlin 60 dominate the semi-auto rimfires at popular prices, CZ dominates the bolt actions, and probably a coin toss between the Hennry and Marlin for lever actions.