The size of the pot will make a great deal of difference to the result. Tall narrow pots—stockpots—rotate the liquid over and around the ingredients for maximum flavor extraction. The diameter of any pot will also result in a specific amount of evaporation.
A pot that is large enough to hold all the ingredients comfortably without spreading them out too much is ideal. These are what I use.
My preference is for stainless-steel pots with a good mild-steel sandwich on the bottom or lined-copper pots. Glazed earthenware and heavy enameled iron can be used. Aluminum is a no-no except for large amounts of stock without wine or vegetables.