Quick and simple stock pot recommendations: a good thick bottom, large in volume, handles & a lid. Thick bottom is the most important, allowing a more even heat for easier heat control (so you don't overboil).
For the best stock pots, you don’t need anything expensive or fancy, and a good one will often have a lifetime guarantee. Stainless steel is generally considered the best material over higher end materials. The reason you don’t need or want something like copper or tri-ply is because thermal mass or evenness of heat distribution are not relevant when heating large liters of liquid over several hours, which are important for searing or sautéing.
In general, a stock pot is pretty simple, but some features might matter more than others. A stock pot that comes with a strainer basket and a steamer basket with a fine mesh, type chinoise is great too, for pasta, etc.
In terms of size, the 16 gets the most use aside from a pressure cooker in making stock. For home use, stockpots come in a range of sizes, usually from 8 to 20 quarts. For most home kitchen tasks, we think a 16-quart stockpot is an ideal size.
Comfortable, sure handles on a stockpot are important, especially when a full 12-quart pot can weigh about 23 pounds—losing your grip on one when it’s full of boiling liquid is a potentially catastrophic kitchen accident. A good stockpot should have handles that are easy to grab both barehanded and while wearing chunky oven mitts (or with kitchen towels), and you should feel in control of the pot when walking around and while pouring out the contents.