As of a couple years ago the 22r blocks were available new. Dan is right, you get a block, pistons and a crank. To assemble a new motor you need pretty much every other part of the motor.
That pile of parts looks something like this:
View attachment 1066236
And yes that pile is what several thousand dollars looks like.
Do not go reman. They generally are all just a block that is punched out to as large an over bore as they can fit, same with bearings, then everything is stuffed back together. Any issues and the motor is a boat anchor.
If you can stand the downtime, your better off finding a good block, yours if it is in good shape, over bore as little as possible. Mild cam, valve job and quality parts with tight tolerances will get you the max out of the motor. Unless you get into turbos and other crazy stuff, about 120-130 reliable hp is going to be the spot to aim for. don't expect more than 150.
Again, look for a good local shop, stay away from remans from the big boxes, minimize the over bore and use good parts and you should end up with a solid little motor.