I have a motley crue of pots as well 
CopperChef square pan. Good size , non-stick. Came with a wire basket but you cannot put the lid on with the basket . I have a deep fat fryer and a steamer so didn't need the wire basket.
One from QVC , stone lined , brilliant
Frying pan from HomeSense/TKMaxx , stone-lined , Brabantia. Really good , non-stick (but in there its the luck of the draw what they have)
An ancient steamer (I think from Debenhams) must be over 25 years old , still going strong
Little milkpan (non stick) picked up in Ikea Bargains bit . It''s an Ikea 365 , goes in the diswasher , I think I'd look in Ikea for new pans .
I coveted some of the Sainsbury really heavy grade non -stick, but they are handwash (so wouldn't be welcome here)
Had some Costco Proline , ok for a while ( frying pans , large+small) but lost their non-stick.