A good cheap rifle in 22 cal? Do you want a semi auto? Or a boltgun?
The 10/22 suggested by nick is a great choice. Totally customizable. You can deck it out in just about any configuration you want. Parts for it everywhere. Everyone sells them. I think you can even get them at Wal*Mart. .22lr is a very common round. Every sporting good store in the country stocks it, along with most "super" / "mega" style stores.
The CZ 452
is a really good little .22 cal bolt gun. Very nice. It's a little more expensive than buying a 10/22 however.
Companies like Kimber and Sako will come up in discussion, and they all make fine weapons, but they are all pretty spendy.
The benefit of a boltgun, especially for young, or new, shooters is that you learn one round at a time. Control. Single shot. Single result. Load a new round. No temptation to fire off a whole mag and "see how you did".
What kind of budget are you looking to spend?