Ply count is mostly a marketing gimmick. 3-5-7 ply does not matter, but what does matter is how much total Aluminum or Copper you shove into the core of the pan. Here's an example:
Two pans are 3.5mm total thickness. One is 3-ply, consisting of 2.5mm Aluminum and 1mm Stainless total. The other is 7-ply, with 1.5mm Aluminum and 2mm Stainless. The 7-ply pan will perform worse, because despite all the layers, at the end of the day the Aluminum to Stainless "ratio" is way worse than the simpler 3-ply. In fact, a 2-ply pan with 3mm Aluminum and .5mm Stainless interior would be even better than the 3-ply. Less layers, but a better Aluminum to Stainless ratio. So never get caught up in ply count, and instead ask "Ok so how much Copper or Aluminum do they actually use?"
With that said, most good Stainless tri-ply pans are fairly equivalent to each other (I would skip Anolon, Calphalon, and some others because they cut corners and use noticeably less Aluminum). There are thicker pans from makers like Demeyere, but you start to pay quite a premium for it. Get a set that has the most useful pieces for how you plan to cook, and you should do fine. 5-6 pieces with lids that you plan to use everyday, is much better than 7-8 pieces where you almost never use 1-2 of the extra pieces.
All-Clad D3, Cuisinart, Tramontina, and the basic Zwilling set are all very similar to each other in performance. This Tramontina Set from Costco is probably the best bang for buck you can get in Stainless atm. Similar would be Cuisinart Multiclad Pro, which is normally available for $220-300. Most of the options you listed are fine, although skip KitchenAid and Viking. They are overpriced for what you are getting.
What you want is tri-ply stainless steel. It holds up beautifully and cooks better than anything else.
Look at sets from Tramontina and Cuisinart.
We’re fortunate enough to have a pro chef in the family. He shows up on the Food Network a few times a year. One of his good friends is a James Beard winner. Plus I’ve met dozens of other pro chefs through them, people who are amazing cooks.
Almost all of them use tri-ply stainless. It holds up in industrial kitchens, cooks well, and you don’t have to be all precious about it, like cast iron.
Reviews have shown that Tramontina and Cuisinart tri-ply works about as well as the much more expensive All-Clad. So pick up one of these sets. They’re what the pros use and they’re BIFL. You’ll never have to replace them.
These Tramontina sets from Costco and Sams are typically what I recommend for best overall value in clad stainless pans. Similar option that isn't always available or on sale for similar pricing: Cuisinart MCP. Same thing but smaller if space is a concern.
They are not necessarily the best performing sets, but they are the value kings atm. All-Clad D3 for example generally isn't a big step up in performance, but it can be nicer overall QC or fit and finish. Any of those sets are practically lifetime worthy, so it's up to you to decide how much performance or attention to detail you really need from the cookware.
If you want stainless, I'd look at Cuisinart MCP 10 / 12-pc or some options from Tramontina. If you have Costco or Sam's Club nearby, they often have similar sets that can be good value as well.
Example: https://www.amazon.com/Cuisinart-MCP-12N-Multiclad-Stainless-12-Piece/dp/B009JXPS6U/
That's a good starter set that isn't much worse than All-Clad, and noticeably better than most disc-bottom cookware sets in a similar price category.