A regular electric oven uses a large coiled resistor as a heating element. A large electric current is passed through this element which generates heat, similar to the tungsten filament of an incandescent light bulb.
An induction stove doesn't actually generate heat itself, but rather induces it the pot or pan. It does this using a rapidly oscillating magnetic field. This field induces an electric current in a ferromagnetic pan which generates heat, thus heating the food.
Induction stoves are faster, safer, and more energy efficient than traditional electric stoves. It requires significantly less electricity to create the magnetic field than it does to drive enough current through a resistor to make it heat up. They are safer because they don't actually generate heat themselves. After taking a pot off the "burner" (glass surface) it quickly begins to cool.
With regards to differences in the cooking process, there's not much. You just need to be aware that it heats up much more quickly and cools down much more quickly than a traditional electric stove. It does affect your choice of pans however. All aluminum pans will not work, nor will some lower quality stainless steel ones. If a magnet sticks to the pan then it will work just fine. The pan must also have a flat bottom to make full contact with the surface.
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).
Best Answer
The concentric rings can serve a variety of purposes. In addition to helping to prevent the pan from sliding, they increase the surface area of the bottom of the pan, which helps it to get heat more efficiently from a gas range.
On some pans, these concentric rings are made of different metals (aluminum or copper) and act to more effectively spread heat around the pan.
I have used pans with textured bottoms on ceramic ranges before with no problems. As always, you will want to avoid repeated shaking motions (say, popcorn) but it's otherwise not a big deal either way.