Tramontina lid stuck to pot

Modifying your original terms:

Size: 2-3 quart/liter. I consider 2.5 quarts to be ideal.

Material: Two options: hard-anodized aluminum nonstick, OR stainless-steel interior/exterior. With stainless, it should have either an encapsulated aluminum disk base or a tri-ply construction (aluminum layered with stainless)

Bottom: Thick is good, and you absolutely must have aluminum here for conduction

Handle: stainless is good, as long as it stays relatively cool. The handle absolutely must be riveted on, with thick rivets. Screws, glue, or welded handles do not last long-term. Tack-welded handles are the bane of the restaurant I work for right now; we've had several handles snap off in the last year.

Additional things to look for:

Weight: HEAVY. You want fairly thick cookware for even heating, but most of that weight should be from thickness of the aluminum disk.

Design: A flared lip around the pot, to facilitate clean pouring.

Shape: I'm partial to shallow designs, which flare out at the top. Although it's nonstick and not stainless, I love my Calphalon Contemporary shallow 2.5 qt saucepan for it's extra-flared design. This lets it transmit heat more efficiently from the range, and allows it to safely hold a larger capacity of food. It also allows for faster and cleaner reduction of sauces.

Lid: TEMPERED GLASS with a handle on top, and a flange to help seal tightly on the pot/pan. Tempered glass is very durable and lets you see the progress of your cooking without releasing the steam. The handle also remains cool, so you don't burn yourself on it; this is the second problem I have with solid stainless lids on many premium cookware lines (All Clad, and most manufacturers' tri-ply products).

While all of these are large pots (or may at least come in large sizes) they have different purposes, which lead to differences in typical construction.

• Saucepans are intended for general purpose cookery, and usually have solid construction, and permit searing in the pot, reducing, and a variety of other tasks.

  They are the most difficult to characterize as there is tremendous variation in quality levels and design among the products available.

• Stock pots are purpose built to make large quantities of stock. Since they are not used for searing typically, and liquids circulate via convection making hot spots not a priority, they are typically constructed from thinner metals (steal or aluminum) and don't have good general purpose cooking qualities.

  The main virtues in a stock part are low cost, size, and light weight.

• Dutch ovens (at least real Dutch ovens) are a legacy from the time when cooking was done in hearth or campfire. They are designed to be nestled into the coals or embers, with more coals or embers placed on top of the lid, creating a hot oven like interior--thus the name.

  True quality Dutch ovens will be fairly thick, usually cast iron, possibly enameled, and may have little legs to help nestle it into the fire above the coals; similarly, a the lid may actually fit into the pot, allowing coals to easily be piled on top.

  Dutch overs are actually fairly versatile cooking implements, and can serve for searing, roasting, braising, stewing, biscuit making, soup making, and even some bread applications even in the modern kitchen. Many are large enough to make stock in for home purposes, although they are not absolutely ideal for the task.

You will have to ask yourself, given your own cooking patterns, would the general versatility of a dutch oven, or the size of a stock pot serve you better. None of the sets you linked to has a true dutch oven, however; the one that purports to be a dutch oven has a glass lid! It might be an okay pot, it is not one I would ever choose.

For stainless steel products (without the specialized legs and concave lid to nest coals in), there is very little difference between a dutch oven and a very large sauce pan.