870 or 500 combo would be best.
There is no one size fits all when it comes to shotguns. When you find the Holy Grail of HD guns, it gives up ground for hunting purposes, and vice versa.
The only option you have is to make a list of your must have options and those you can live without out or live with at a diminsihed capacity.
Possibly the closest you could come up with would be a 22"-24" barreled turkey gun with the addition of a collapsible butt stock, you could be as close to a do it all shotgun for your intended uses.
NRA Life Member