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How deep is your pocket? If the budget allows, have a peek at a Burris Timberline. Fairly compact, yet has a max of 14x for target work. AO lets you dial in for all ranges. Quite highly rated over at Rimfire Central. Mine is on a Belgian Browning T Bolt.
A 597?…accuracy is probably good out to what 50 maybe 70yrds? For your application(s) ^^^ I think a fixed 4x power scope would suffice. Quick, compact and light especially if you intend on mounting a bi-pod on the rifle and carrying it in the woods.
For around $40 I'm happy with a fixed 4x power Simmons 22mag on my (50yrd) .22lr plinker….YMMV