Saucepans (or just "pots") are vessels with vertical sides about the same height
as their diameter, used for simmering or boiling. Saucepans generally have one long
handle. It has a round base, tall straight sides and a tight fitting lid. That is
a classic sauce pan. And although many of them are made today with nonstick materials,
the nonsticks are not great for making classic sauces.
Larger pots of the same shape generally have two handles close to the sides of the
pot (so they can be lifted with both hands), and are called sauce-pots or soup pots
(3–12 liters). Saucepans and saucepots are measured by volume (usually 1–8 L). While
saucepots often resemble dutch ovens in shape, they do not have the same heat capacity
HandleYou want a medium handle for a few reasons. You do move the pan around some on top of the burner. I also find myself holding on to the handle when I reduce a sauce, mash potatoes or saute ingredients. Part of that feeling good in your hand associates with the handle too. You may be lifting the pan to go to the sink or lifting it to sauce a plate so the handle should feel secure.
As with all your pans, you want a cover for your pan that fits tight. Besides using sauce pan for making sauces, you may find yourself using it for braising where a tight cover is important. If you have pans whose lids don't fit that well, try covering it with a piece of aluminum foil before placing the lid on top. Some lids come with knobs on top. I like the large loops that I can grab with my oven mitt or more likely with my kitchen tongs.