Budget is important. If price is no problem, get an Anchutz in the 2K range. I suggest the classic stocked version. I tried four with the rollover when classics were not yet offered. I could not live with them.
The Ruger 10-22 is always a good choice.
Remington has done Marlin no favors since buying them. Go used there and look for the JM proof mark in the barrel, near the receiver. The lever 39A (JM proofed and before rebounding hammers) were generally excellent. Same for 60 and 795.
Remington 5xx models were all great performers. They came in several versions from single shot to match grade target models. I inherited a single shot 510. I recently found a magazine repeater 511 in great condition in a pawn shop for forty bucks. Super price and it shoots tiny groups. Past experience with a Junior target model and with a 541 deLux sporter were all great. Got to shop used for these. New Remingtons just don't do it for me.
Going new for a bolt gun, do not overlook the CZ offerings. Great reputations.
I hear mixed reports on the Henry lever guns. Some good some not so much.
Same on the Rossi pumps-mixed.
Good shopping, jack