For a lightweight 20 gauge in the budget category, it’s very difficult to do better than the Stoeger 3020. Trim, light, excellent handling, simple Benelli-style recoil-actuated, reliable, and available in a variety of stock options including a very nice looking wood/bronze Upland Special. Street price is around $500, excellent value.
Winchester’s SX4 is the next worth considering. A gas-operated auto design, the SX4 will soak up recoil for a much more comfortable shooting experience. The SX4 also has a highly adjustable fit. I believe street price is around $900.
The Beretta A400 20 gauge is a significant step up in price, starting at $1300 and rising depending on stock material and finish. However, what you GET for that is Beretta quality and one of the softest-shooting autos on the market. The gas-activated Beretta system soaks up so much recoil. Also, Beretta has stock shims to adjust the stock drop, another big plus in terms of being able to customize fit.
A Remington 1100 I feel is not a fit for a one-gun solution because the 1100 requires a separate barrel to shoot 3-inch shells, they could not shoot 2.75 and 3-inch shells interchangeably. Unless you could find an 1100 so cheap that the extra barrel could be justified, of course.
The big hurdle here is the rifled slug barrel. Very difficult to find a lower-price-category 20 gauge that has a slug barrel available, I don’t believe any of the above options has one. You may have to pursue a 2 gun solution here. I personally would not want to give up the trimmer, lighter, softer shooting 20 gauge. I’d look for a used slug gun that is already set up.
A 20 is plenty for turkeys, obviously, like any hunting, the skill is in bringing the birds in close enough.
Grouse.