I think there are a few tips to use when selecting cookware but beyond that, much of it is personal preference. I use primarily tri-ply stainless. Most of mine is Calphalon, with a few pieces of All-Clad and Cuisinart. I like that the stay-cool handles for on top of the stove and I also like that they can go in the oven, too. Most of my pots have glass lids, which I like so I can see what's happening in ther. (I'm fairly new to real cooking so I need to watch things closely.) I like that no matter what I burn, I can clean it with BarKeepers Friend and it looks new again.
I have a couple of cast iron skillets and a flat grill. They are invaluable for things that need high, even heat for a great sear. But because they are black, I don't use them for much else, even though you can, because it's hard for me to tell when things are starting to burn.
That is the reason I didn't choose anodized or non-stick.
That said, I have several pieces of Calphalon non-stick because my sons prefer to cook with them. They get very good results. My daughter is a vegetarian and all of her cookware is non-stick Calphalon. If they need high heat for things, they use their grill outside.
There is no one perfect cookware for everyone. If I were you, I'd buy a piece of each and try them for a while. You may end up wanting a few pieces of each or you may decide you love one type and buy only that. As far as sets, unless you find a set that has only items you need and will use, I would suggest buying piece at a time.
Good luck and let us know what you decided on!