The most versatile pot that you can ever have in your kitchen would be the Dutch oven. Not only can you do the obvious of stovetop braising, stewing, and boiling, but the Dutch oven’s weight and material are ideal for oven searing, frying, sautéing, and even oven braising and baking bread. Cast iron has the most efficient heat retention properties than any other pan material out there.

That means when it gets hot, it stays hot. You don’t have to worry much about the pot losing too much heat when you hit it with cold meat, or the temperature of the oil dropping too much when frying some chicken. If someone was to rob you of all your cooking equipment but lets you choose one pot to hold on to, you best choose the Dutch oven lest your life depend on it. It’s the one pot that you really need to survive. All others simply make life easier.

Compared to all your options, a Lodge brand Dutch oven is a real decent budget but that’ll do everything you need. My Lodge Dutch oven was the first pot I’ve owned and its treated me well. It has its own battle scars of wine stains from long braises and polymerized oil from splatters of deep fries. It’s got character.

If you want to go for the the real quality stuff, Le Creuset is the standard. It’s a little pricey if you’re on a budget, but it’ll last you multiple lifetimes. Think of your kids!