Now that all three of my kids are eating with regular plates and utensils, I both use the dishwasher and handwash -- the dishwasher gets plates, cups, bowls, flatware -- whatever I have *many* multiples of and the "singles" -- pots, pans, spatulas, knives, etc -- are hand washed. I usually run the dishwasher every two or three days, less often if we eat out a lot.
Sometimes, if the top rack is full but the bottom isn't, I might throw in a pot or two to fill it up so that I can run it. But most of the time, I handwash the pots, knives and cooking spatulas that we use every day.
Our most-used pots are the hard anodized kind, like Calphalon, except that it's the JCPenney brand (Cooks, I think). We used to have T-Fal, but I got tired of the non-stick coating chipping off all the time. (Our smaller pots are still T-Fal -- we don't use them much because we have Pyrex Visions pots in those sizes that we use instead. We keep them because on very rare occasions it is nice to have an extra pot or two.)
DH's grandmother requested a small T-Fal skillet and saucepan, and we bought her the hard anodized ones, with gift receipts. We're not sure why she specified T-Fal, so we used our own judgement.
I hope your daughter enjoys her new cookware! For the other comments, I have to admit I'm a bit intimidated by cast-iron, having never known anyone that has one.