$500-$600
The value of a Remington model 600 .222 caliber depends on the condition of the gun. One in excellent condition is worth approximately $500, as of 2014.
remington 725 caliber 222 bolt action excellant condition
400 USD
Winchester didn't make it, Remington did. Worth 222-350 depending on condition and lust level of buyer
The Remington model 720 rifle was never offered in the 222 chambering. While it would have been technically possible to convert, the work required would have been totally out of any reasonable proportion to the result. Perhaps you actually intended to refer to the Remington Model 722 which was produced in that caliber. Price guides area available for reference to the current value for one of these rifles.
50-350 usd
$600-$700 IMHO
100-300 US Dollars
Looks like it's 1-14.
Remington, Winchester, Sako to name a few
I sold one in 2002 for $450. It was VG condition, bought new in 1976 for $160 and used very little.