Rupestris;
The .22 pump that you're referring to is almost certainly the Remington model 141A 'gamemaster', a forerunner of the 572A & the 572BDL.
MaterDei;
Although I'm no fan of Remington, I'd have to concur that a used 572A Fieldmaster in good shape would be a fine thing to get ahold of. Used in very good to excellent shape, one should be in the $150.00 to $200.00 range & worth the money. Personally, I'd rather have the A than the BDL. The BDL is flashier & books for more money, but does not offer any operating advantages. The easiest way to immediately tell the two apart is that the BDL has a swept-back ray-gun type front sight, the A is a normal dovetail bead.
I don't know as a Henry would be a mistake, but me, I'd look elsewhere.
900F