You can cook anything in stainless steel. Believe it's the aluminum products you have to be concerned with when cooking tomato-based sauces.

I would be looking at a good quality non stick pan....look for one with an aluminum body because it conducts heat better than stainless does. I like Meyer professional....and a 10 inch skillet should do fine for cooking chicken and making a quick tomato sauce. Don't know what you mean about low heat stir fry....but do remember that you shouldn't be using high heat with a non stick pan.
Linda C

Here is a link that might be useful: professioinal cook ware

I cook tomato based foods all the time in All Clad Stainless and it's over 15 years old and still perfect. I also use my 12" Non Stick Calphalon Everyday Pan, everyday :) for slow frying and sause preparation. If I had to buy one pan, I would pick the 12" Non Stick Everyday Pan, it's perfect for frying as it is aluminum, it's large enough to cook sause, it cleans easily, it is not too heavy and it has two handles so no wrist problems.

I don't think I've ever heard of anything you can't cook in stainless steel.

Tomato-based sauces can strip seasoning off of cast iron and maybe make the sauce taste funny if you simmer it long enough.

Not sure what t-fal's non-stick surface is, but if it's wearing off you're probably eating it. Not something I'd want inside me.