We like our home fry potatoes in relatively small, bite-sized chunks. They need to be tender, but not falling apart into mush. Best is when the potatoes have been left sitting in the pan for just slightly too long so one side has totally crisped to the point where it's almost burned. It's surprisingly difficult to intentionally burn your home fries!
We're also of the mind that home fries should be relatively unadulterated by other seasonings. We like them salted and with a dash of paprika and cayenne - nothing fancy. We'll occasionally allow some diced onion to join the potatoes, but that's about it. To us, versions that mix in all sorts of other vegetables are missing the point.
We've had the best luck cooking home fries in our cast iron skillet with the heat on medium-high. We brown the potatoes in a bit of butter or (even better) bacon fat, and then cover the pan for a few minutes until the potatoes are tender. Then with the lid off, we go for that crisping, almost-burnt stage.
What's your favorite style of home fries?