What to look for in a pot? What to look for in a pot. I'm supposing somebody that's just starting to live alone or a couple. Help me complete this list.

Size: small, but not too small. Maybe 2L or 3L.

Material: Stainless steel with a thick bottom. As you are going to buy only one pot to begin with, spend some extra money on quality. 

Bottom: A thick bottom is a must on electric or ceramic stoves as they don't bend out of shape so easily. Also, a thick bottom is handy for slow cooking as the heat diffuses more evenly.

Handle: Same material, stainless steel. This is handy if you want to put the pot in the oven. Look at the fixture to the pot, it must be riveted on, with thick rivets.

Stove: if it's going to be induction - Glass, Ceramics, All Aluminum etc. are all out.

Price: Not too expensive. 20€ - 30€?

What am I forgetting?
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).