I discovered that a lot of the clad pots and pans that have aluminum sandwiched between two layers of stainless have 18/10 stainless on the interior of the pan and 18/0 on the exterior. I suppose that the reason for the cheap stainless on the outside (aside from cost) is for induction cooking. I don't have an induction stove, and don't plan to buy one. I have a gas range. So 18/10 sounds better, but the pans I'm looking at have 18/0 on the outside. Does it make that much of a difference?

Also, how much difference is there between 18/8 and 18/10? (Most of the pans I'm looking at have 18/10, but some say 18/8.)

The magnetic properties of stainless steel is determined by it's crystalinne properties. There are two crystaline forms of interest to cooks-austenitic and martensitic.

Pots and pans are generally made of austenitic stainless. It is the most common form of stainless, and is most commonly seen as 18/10 or 18/8, though 18/0 is also available. During manufacturing, it is cooled slowly. It is more corrosion-resistanic because of the large amounts of Chromium and Nickel.

Stainless knives are usually Martensitic stainless. It is cooled rapidly which changes it's crytalline structure, and is thus (usually) magnetic. It contains less Chromium than austenitic steels, and much less Nickel. Howver, it is machainable (austenitic is generally not) and magnetic.

Thus, in a kitchen, we (usually) have pans made of austenitic and knives of martensitic stainless. This is why most stainless pots will not hold a kitchen magnet, but knives can be stored on a magnetic strip.