Tri-Ply good investment
As a chef, and an owner of many brands of cookware, tri-ply (or more-ply) is a good way to insure even conduction of heat across the bottom of your pan reducing the possibility of burning the food you spend good money on. There is, however a point where function does not balance with cost (and many companies pander to the unknowing by saying "we have 7 ply construction", etc.) There are a couple of points you need to consider in construction that are quite important, however.... handles attached SOLIDLY on the side of the pan (a safety concern), a HEAVY bottom layer (more even heating), oven proof (no plastic or wood handles which may warp/burn), and DURABLE lids (so you are never going to have to buy another lid, and another, and another). All clad is great, as the heat transfers up the side of the pan heating soups, etc. that much faster.... but is not an essential to a good, functional, and more than adequate home use pan. I am not going to suggest particular brands, as you may not find these available to you in your locale, and I do not want to give any particular brands a free plug, but the heavier, the sturdier, the better.
Use wise- SS (stainless steel) is functionally very different than nonstick. It will stick with egg almost every time, so keep one nonstick fry pan available for egg use (or even better cast iron or carbon steel). However there are tricks to use SS with frying meats, etc. 1)keep the heat on medium, no more! 2)preheat the pan for a minute or two before adding anything to the pan, especially if it is an electric stove 3)add oil and heat till light smokeyness rises from pan (you must use oil/butter to some degree) 4)add chicken breast/pork chop/steak now, and LEAVE IT ALONE for 2-3 minutes.... DO NOT POKE/PROD/MOVE!! 5)after the 3 min. check the brownness now;if brown, flip and again LEAVE 2-3 minutes;if not brown enough try another min or two. 6)from this point you can add sauce, veggies, or just put into hot oven for another 5-10 to cook through (as to your preference).
Sauces/soups/ and liquid cooking is much easier-just make sure to use Med heat (or at VERY most med.high heat), and burnt/scortched foods will be nearly non existant if you don't forget your pan on the stove. I can go into so much more detail, but I am out of time for the moment, and I hope this gets you off on the right foot in looking for your new SS cookware.