There's no universal answer here, different 870s shoot different shells best. You can take two identical shotguns, even 870s, off the line with consecutive serial numbers, and the chances are slim that any slug will shoot equally well from both.
I've been slug hunting for close to 40 years. This year is the first time I've two shotguns that "Like" the same slug.
However, you might start, for unrifled bbls, with a 2 3/4 slug,not 3 inch. No deer, not even those big, cornfed Midwest bucks, will be able to tell if they were shot with a 2 3/4" or a more costly 3 inch slug. Less kick with the 2 3/4" also.
The doe I took yesterday was taken with a 2 3/4" slug. A short blood trail Ray Charles could follow...
Good potential candidates for the slug of choice would include the Federal and Winchester Forster types, and the Brennekes. Bad choice, any sabot.They work best in rifled bbls.
Best turkey loads are equally capricious. One that's patterned well for me is the Remington Duplex, 4X6 load.
But maybe more serious turkey hunters may be able to help more here.