What to look for in a 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).

You probably won't want a stainless steel handle, as that transfers heat well, which means holding the pot could be uncomfortable. Look for one with a handle made out of some strong plastic.

Otherwise, you seem to have everything...

I ask if you planned to use these pots on an induction range, you responded: it might be.

The point is that induction ranges require specific pots in order to work. You might look into these requirements to further inform your decision.

Glass, Ceramics, All Aluminum etc. are all out.

It's a tough question for just 1 pot. I would only get a metal handle if you intend to do a lot of oven broiling or baking w/ it also (Like searing the roast and then braising it).

All of that being said, I think cast iron is a great multi-purposer (stir fry, shallow and deep frying, sautee'ing, etc...) It would be oven safe and it's thick enough that if you have cheap appliances, it offers a buffer. It's obviously terrible omelets or something, but from your comment @Thursagen, it looks like you have oven aspirations...

(another awesome thing about cast iron is the fact that it will get "seasoned" over time, just make sure you season it properly the first time according to the manufactures directions and hand wash it henceforth)

You've got most of the big points, but I would be a little bit more specific about the handles. Stainless steel handles will allow you to put the pot in the oven, but they will also transfer heat very well and will make the pot harder to pick up after it's been on the stove for a while. If you decide to go with stainless steel handles, be sure to get a pot with handles large enough to accommodate your hands with thick potholders, because you will need them.

Also, if you're just starting out, stainless steel is a reliable, budget-friendly material. But if you really want to invest in quality early, you'll want to look into pots with copper or aluminum cores, as they will transfer heat significantly better and more consistently than solid stainless steel.

For more in-depth information about how to select a stockpot to fit your cooking style, check out this article.