At the bottom end on cost the Crickett or Chipmunk; single shot, bolt action, manual cocking 22. Its lots of fun, and teaches you a lot about the basic working of a gun. single shot, not semi-auto Crickett 22LR little single shot bolt action .22.
http://www.crickett.com/crickett_22_pistol.php
Chipmunk 22LR same gun, also sold under the name Chipmunk some interesting variations, and different stocks.
http://www.chipmunkrifles.com/chipmunk_22_pistol.php
For cheep plinking the Beretta Neos, VERY easy to clean and shoots/runs on most any ammo, great price. Put a little red dot on it for $20 and you have a super fun plinker. I love mine!
Next up in price and quality are Rugar, Buckmark, and Beretta 87 Target.
If you are a tinkerer and like to work with triggers, options, and customizations, the Rugar is the only way to go. LOTS of options like triggers, grips, even high end match quality improvements. (But then, so much for the price point) Great for those who like to customize or just want a relable accurate shooter. Some people have trouble with take down and re-assembly, there are a few tricks to it, but not impossible. There have been more than a few brought into the local gun store in pieces begging for help : ).
Buckmark also has a fair number of models and options. Probably a close neck and neck as to which is most popular with the Rugar line.
Beretta 87, not as well known but very nice gun.
For high end accuracy at a price you can still live with, the HAMMERLI XESSE; match grade chamber, barrel and trigger. Intro level gun for genuine
target competition. starting at under $700 ($699 : ) This gun is designed to run on sub-sonic ammo. Use target grade, the gun deserves it.
For beauty, collectability, and fantastic function and accuracy, the S&W model 41 or the Browning Medalist. The S&W is a lot easier to find. Both have been used in top international matches. Both are amazingly accurate. Few shooters will ever be better than these guns. The S&W is still used in matches. The Medalist has been out of production for too long, you won't see too many of them on the fireing line. Like all target guns, they are intended to use sub-sonic ammo.
For serious modern target shooting, there are some amazing guns from Anschutz, Walther, Pardini, Hammerli, Morini, Feinwerkbau, and others. Price about $2,000 and up, mostly up. True Olympic winning guns in this mix.
In whole separate categories are little pocket .22 pistols and conversion kits.
Pocket 22s are just that, very small guns, ranging from VERY cheap (cheaply made too) to the small Walther and the like.
Conversion kits are nice for running some practice, but by and large, they need to run on high velocity ammo to have enough oomph to cycle the action. High velocity mini-mags and the like.
Also consider: If you just want low cost and some basic gun handling skills, there are also air guns, and airsoft guns that could be an option. Many are available in replica models, (ex I have a H&K USP in airsoft that is same weight and controls as my real 45) They are much cheaper to operate that 22 and can be safely shot at home in the yard or with proper back stop indoors. Airsoft is a lot cheaper than 22 and 22 ammo is a little hard to get right now (has been for a while) Seems like lots of folks have been looking for a cheaper way to shoot. The days of 550 round box for $4.99 are long gone.