Mauviel makes four different lines of copper - heavy or light gauge, and copper or tin lined in either gauge. They also used to make an intermediate weight line of tin-lined iron-handled cookware, but that was discontinued some time ago.
The heavy gauge will range from about 2.5 to 3 mm thick and have iron handles - that's what you want. The stainless lining is more durable and more expensive. Some claim that it defeats the heat-conductive properties of the copper, but that's really not the case, at least not noticeably. The tin lining is traditional, but it's more fragile than steel and will wear over time and need to be retinned, which is expensive.
The light gauge ranges from about 1.5 to 2 mm. It will have brass handles and be less expensive, of course. It cooks quite well, but the heavy gauge is really preferable.
I agree that you should also have some cast iron pans around, probably a couple of large skillets and a Dutch oven. Cast iron is actually a rather poor conductor of heat, but it's made very thick so it can heat more-or-less evenly (anyone who thinks it really heats evenly has obviously never cooked in a large 3.5-mm thick copper sautoir), and it does have a lot of thermal mass, so it retains heat very well - good for some applications, not so good for others.
A personality of a fish is a combination of its thickness, texture, fat content, and flavor. Understanding these 4 elements will help you choose the right cooking methods, and find appropriate substitutes when a particular fish is not available
Recipes techniques savor a world of authentic cuisine