A heavy-duty mixer such as a Kitchen Aid is essential for the recipes here. I suppose you could get away with a heavy-duty hand mixer, but it would be less convenient to use. If you are investing in a stand mixer, go all the way and buy an extra bowl and whisk. They will save you so much time in the first year you use the mixer that they will more than pay for themselves.
A food processor is essential for grinding nuts and mixing many doughs. My first choice of machine for mixing most pastry doughs is the food processor. Use the metal blade for pureeing, grinding, and pastry doughs, and the plastic one for most yeast doughs.