Clarification needed on pots and pans in the dishwasher

So I know from a previous question that you are ok putting glass, glazed ceramics, silicone and stainless steel in the dishwasher, and that you should avoid putting non-stick coated, aluminium, copper, cast-iron, tin, wood, unglazed ceramics, etc in the dishwasher.

However, I'm in the market for a new set of pots and pans, and would like to know what I should be aiming for. At the moment, I have a skillet set:

• 4 inch non-stick - ruined


• 6 inch non-stick - ruined


• 8 inch non-stick - ruined


• 12 inch non-stick - not ruined


• 12 inch cast iron skillet - babied

During previous bouts of laziness, I've put them in the dishwasher and thus ruined the non-stick coating on most of them (the cast iron skillet is babied and never goes into the dishwasher). I also have a 14 quart pot, which is showing its age, and an 8 quart pot which had its bottom corroded to the point where a hole appeared (thus, leaky pot).

As an avid (and lazy when it comes to washing dishes) home cook, what should I be looking for in a set of pots and pans? At a minimum, what should I have in terms of sizes and types. I'd prefer to purchase them separately rather than buying a set (budget is not a limiting factor). Additionally, I'd love for them to be dishwasher safe, but I can add a few more 'hand wash only' items like my cast iron skillet.