I would quite like to get hold of a large stock pot with a thick base so I can make things like preserves as well, but whenever I look at kitchenware in my local shops (I'm in NZ if that makes a difference) the stock pots I see always have very thin bases, no thicker than the walls. Are the ones with heavier bases called something else, or am I just finding poor quality pots?
I don’t know if the nomenclature is different in New Zealand, but you might consider an enameled ‘Dutch oven’. They’re typically cast iron, coated in enamel to make them easier to clean / less reactive. Unfortunately, they’re quite heavy, and they don’t tend to have the same proportions as a stock pot (they’re more squat versus the tall and skinny stock pots). And the ones from France tend to be quite expensive, but there are a lot of alternative brands these days
Another option is ‘tri-ply’ pans in which they look like stainless steel, but it’s actually stainless around a core of some more thermally conductive material, such as copper. ‘All clad’ is the original brand for this, but some more reasonable priced competitors have been available for the past 5 years or so
Then there are lots of brands that put a disk of copper or aluminum on the bottom of the pan. It’s usually pretty obvious on inspection— either a different color on the outside bottom, or a blatant disk that doesn’t smoothly transition to the sides of the pot
I would recommend going to a store, finding a sales person and specifically explaining what you want. It’s entirely possible that they won’t have any true ‘stock pots’ like you’re looking for, but they likely have pots in slightly different form factors that match your need. And you might want to add a spatter screen.