I just moved to Benton, in Marshall County. Anybody know of pistol, rifle, and skeet/trap/clay ranges nearby?

Land Between the Lakes near the Golden Pond Visitor Center. One hundred yards and free but you must reserve it at the visitors center.

Caldwell County Sportmans Club near Princeton. Free and 235 yards. The club uses it on the 1st, 3rd, and 4th Sundays but other than that it is open and uncontrolled.

These are the only two I actually have used.

Bush Roads Sporting Clays:  6 or so miles off I-24 on Hwy 139 near Cadiz. Open to the public on Sunday afternoons 270-522-0448

Kentucky Regulators Range Cowboy Action Shooting, IDPA and other stuff. In the little town of Boaz between Mayfield and Paducah.

Sorgum Ridge Sporting Clays in Wickliffe, KY 270-335-5400

Eagle Skeet Range (also has Trap and 5 Stand) on the Fort Campbell Army base (but open to the public)

Jackson Purchase Gun Club in Paducah.

Somewhere in or around (1) Calvert City and (2) Fairdealing there is (or once was) a Trap/Skeet club. Once you find  a local trap shooter or two surely they'll know more about these ranges.

A little farther up I-24 is the Rend Lake Shooting Complex

I've shot several times (and still do) at Bush Road, Kentucky Regulators, Eagle Skeet, and Rend Lake. No problems at any of them.