For my wife and our daughter of seven years age, I know I will want to cook about 10 lbs of potatoes every month or so for frozen mashed pototoes and make a pizza dough about once I week for a couple pizzas. What would be a good Kitchenaide model for this kind of minimal use, money is kind of an issue but I dont want to come up weak on power.
Stand up mixer
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In recent years KAs have become notorious for not standing up to the demands of making dough. Turns out Whirlpool started using a nylon gear in the new models. Not sure why but apparently this nylon gear breaks under the stress of making dough quite a lot. If I were you I wouldn't even consider buying a model that doesn't have all metal gears. The highest wattage you can afford the better. I have a Professional HD 5 qt stand model (not really a 'professional' model) that is supposed to be 500 watts and it makes some outrageous noises when making just pizza dough but it does manage to do it. I probably wouldn't go making triple batches of dough in it though. Got a good deal on sale at Costco, but if I had it to do over again I might see if I can find an older model (pre-Whirlpool) used on craigslist or eBay. Then again if I had it to do again I might consider some other models known to handle dough better as well. I'm happy with my KA overall, it doesn't see heavy use and Empire Red certainly does brighten up the kitchen.
You might also look into buying a refurbished one directly from KA. They come with the standard warranty.
Any of the KitchenAid stand mixers will be up to the task... but mashed potatos are generally fairly bad made with a mixer; are you sure you really want to to that? A ricer or food mill would be a better idea for the potatos.