How does your hand/stand mixer's speed effect the texture of your cookies?
Speed would impact in so much as rapid speed helps incorporate air bubbles. These bubbles are important, since they capture and hold CO2 during the rising portion of baking (essentially I like to think about baking in 4 phases: mixing, heating and rising, setting, and cooling).

Usually you use a spatula vs a hand mixer when you A) are using an incredibly dense dough which could damage a mixer, or B) you are concerned about the formation of gluten. Gluten is essentially a good thing in breads, but a bad thing in cakes, and muffins.