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In all honesty, as with a lot of things, a piece of equipment that does multiple things doesn't do any of them as well as a devoted piece of equipment could do. You probably won't find one that suits your desire of doing all of those things AND does a good job of it. Just my opinion.
I agree with this. The best tool I have found for shreading hash browns is the Salad Shooter Pro. Many other devices are too weak.
I use a meat grinder attachment on a table top mixer for making sausage and hamburger, although a dedicated electric meat grinder would be a touch better. I used a hand crank unit for a while and it really sucked for making large quantities of burger or sausage.
As far as a food processor, that is what I use to make salsa or chop onions. It can make mush out of almost anything, so a variable speed model would be a better choice.
Finally, an electric coffee grinder also works as a spice mill. If you have spices that you want to make into smaller particle size, nothing works better.