Which brand is best for a stainless steel cookware set?

There is no “best,” you just need to know what to look for.
18/10 stainless steel is the best. Keeps its luster, highly corrosion resistant, virtually zero reactivity with the food, even acidic ingredients.
Next, look for a thick bottom. The cookware should be heavy. That massive amount of metal traps heat and isn’t easily cooled once heats up. It also distributes heat evenly in a controlled way rather than the thermal energy of the flame passing straight through the pan and into the food, which will cause burning and noticeable hot spots.
You will also want to make sure your pot/pan isn’t just a disc of metal welded crudely onto a receptacle made of another inferior grade of steel. This type of construction is common in inexpensive stainless steel frying pans and skillets and is inferior in terms of thermal conductivity and even distribution of heat. You will have hot and cold spots all over the place.
Expect to have to pay for quality. The manufacturing process for great cookware is by nature more expensive than just welding a disc onto another container.
All-Clad is a big brand, yes, and that does feed into the high cost of the cookware. But it’s not expensive for no reason. All-Clads are reliable, durable, and well-known for great construction and quality. If you can get an All-Clad for cheap or free, that’s a steal. It’s going to last a lifetime.
That being said, you can save a few bucks by getting cookware from another maker that doesn’t have a big brand name but still makes high-quality cookware the right way. This cuts down on the cost of marketing and results in the product being cheaper because the company doesn’t need to make up for marketing by increasing prices.
I stumbled on a brand called Silga at a thrift store and did a ton of research. Really solid quality on its Teknika line. The base is amazingly thick, something like 14mm, which is even thicker than All-Clads. 18/10 steel, great discounts during sales as well. Reinforced and perfectly shaped lips for pouring, lids that are so good they’re practically worth the price even without the pan/pot. Heat conduction is very even, heats reasonably quick, and it stays hot once it heats up. Absolute joy to use and I prefer the feel of the Silga to All-Clad,. The problem is they’re still not cheap. Each pot or pan is easily $150. If not on sale, prices can get well into the $200s or $300s (for the gold ones). But this is currently my favorite brand and line for stainless cookware. Silga Teknika. Not a big online presence, so you have to dig around to find them.
I have a couple of small All-Clads and really want a wok from the discontinued copper line, but those are like $350 and I’m not ready to spend that kind of money…

Non-Stick Cookware Set, Pots and Pans – 8-Piece Set