A pump is excellent for a second shot. Remington has made excellent pump rifles and I find you stay on target in between shots, better than a lever.
That being said I hunt with a Marlin Lever gun. A 336 in .35 Remington caliber. Its accuracy with its micro-groove rifling is sub 1 at 100 yards. I chose this over all my rifles for its short handling ability in dense woods
Its caliber is not for longer than 200 yards though but where I hunt I dont get those long ranges.
It's really only reliable aiming out to about 100 yards. A fine beed on the factory iron sight is sighted right on at 50 yards and a coarser beed gets you on at 100 yards. Much longer than 100 yards you put the sights on the target then raise the barrel up a bit and see where the bullet hits. A poof of dust low means raise the barrel higher for the follow on shot.
It's a terrific rifle for brush and heavier forest and definitely not reasonable for longer open country shots. My shortest deer shot with it was 50 feet and the longest towards 300 yards, blind luck on that.
IMI (Isreali Military Industries) used to produce a pump action in .357 Mag called the Timberwolf; I almost picked one up but the seller wanted way to much. They were out of production by then, so that’s ok...replacement parts would have been hard to come by.