I would never use a mixer for potatoes. I think a ricer/food mill is the way to go. A food proc. is right out.
Leaving the jackets on for boiling does improve the texture and taste of the potatoes. It takes longer to cook them obviously, but I think it is worth it.
Use only whole, cold cubed butter. This improves texture and basically allows you to emulsify the butter into the potato. Melted butter is OK, but doesn't have the same luxurious taste/texture of whole cubed butter. Think of a buerre blanc versus a broken butter sauce.
The puree can get gummy no matter what kind of potatoes are used. The main reason these things get gummy is because the maker fails to keep the mixture HOT. When the starch in the potatoes cools down, it gelatinizes and this is what leads to gummy texture. Nothing can be done to fix it. So, when you are making your potatoes, keep the mixture hot and store it so it won't cool down. That is the number one reason right there. Yukon golds are pefect, IMO, as they have a low-medium starch and a great flavor and texture. Russets work OK as well, but will have a more pronounced "grainly" texture and are more prone to "water-iness."
Things like a tamis are optional and just go to improve texture and remove small lumps, etc.