It depends on how you are defining "22 LR target rifle." Most "22 LR target rifles" are single shot.
It also depends on what you want to do. Sound like you just want "cheap trigger time", and fun/familiarity for practice, and not any competition (smallbore prone, 3-position, rimfire benchrest, rimfire silouette etc). So it sounds like you are looking for a moderately priced 22 LR bolt action sporter.
Marlin 782, 2000,
Remington 521 (or "500" series for single shot/repeaters like 510, 512, 513, 514, 521, or the newer 540 series)
Winchester 320 (310 single shot), 69a, 75 target.
It's up to you and what you want to to. I used to shoot smallbore varsity rifle at a service academy (Anshutz 1413). I like serious target rifles.
I really enjoy range shooting with my Remington 540x, and Win 310 (sporter). I used to have a Win 75 and a couple of Win 69a's, but the trigger and accuracy is better on the Rem 540x. You can probably find a Rem 540x with excellent receiver sights for less than $500. Not cheap, but it is an excellent training platform (and great squirrel rifle).
You can do an great deal of shooting/training/practice with a Remington 510 Matchmaster for ~ $150 or less. Single shot sporter. Will need receiver sights, and drill/tapped receiver for scope, but a good simple accurate rifle.
The Rem 513 is a classic too.
If you find a suitable rifle, try to find one with a grooved receiver for easy scope mounting. Not all Win 69a's or 75's had this feature (or most of the Rem "500 series"-the Rem 540x DOES have a grooved receiver).
Keep it simple, and definitely get a good rifle. It's great practice.
"Behavior accepted is behavior repeated."