I've found it is best not to go for quantity but rather for quality. You're not really ever going to use all of the pans on a consistent basis. I'd recommend an 11 inch pan for the majority of the cooking and a smaller 9 inch pan for stuff like omelets. Then a 2-3 quart sauce pan comes in handy for sauces, small amounts of soup, rice, etc. If you need something bigger like a 6-7 quart pot for soups then just move up to an enameled dutch oven. You can get a pretty good one of those for cheap from Lodge for about $50-$75. And Emeril makes a nice 6 quart blue one for around $99.
All-Clad is the best known name in stainless steel pans. However I think the best quality likely belongs to Demeyere with their Industry 5 pans. Mauviel also makes some pretty good stainless steel pans that rival All-Clad pretty well. Demeyere is part of the Henckel's knife brand. And Henckel's is a very distinguished German knife brand that has been around since the early 1700's. What I like best about Demeyere is that the handles are welded rather than riveted. It makes the pan easier to clean. No cleaning around the rivets. Secondly, Demeyere puts a special finish on their pans that won't tarnish. And they'll also take very high heat. The metal on a Demeyere pan is also thicker for more even heating and they work with the new induction ranges, which are great if you've never tried one.
The set of stainless steel pans that I've had the longest is a set of Kenmore Stainless Steel pans I got from Sears. I got the whole set for like $200. They've actually done very well. I've had them for at least 10 years and they shine basically like a new All-Clad pan still even after a ton of use. The only thing I can say bad about them is that one of the pans did seem to get a bulge on the bottom of the pan where the bottom may have warped or something. The rest of the set is totally fine.
I'm not quite as picky about my pans as I am my knives. There's even one $20 made in china 2 qt sauce pan that is my fave. For some reason it cooks really well and is super easy to clean.
However when it comes to non-stick pans. My favorite by far and away is ScanPan. The stainless steel outside on them will tarnish brown from the heat. But NOTHING and I repeat NOTHING sticks to the inside of them. They are expensive but well worth it.
As far as knives, this is where I'm picky. Because if you have a good quality well designed knife it makes your food prep work a lot easier. My favorite brand of popular knife is Wusthof. They have the best balance and control of any of the popular brands. I like their Wusthof classic line with the full bolster. The full bolster helps give better knife control with a pinch grip. Of the popular brands, Henckels is a close 2nd. A lot of people like Shun, but I can't say I'm a fan. Their knives are on the heavy side I think. Shun puts very sharp edges on their knives. But the blades are often a little too thick too, causing their knives to feel like they stick once you cut so far through.
My favorite knife design is actually sold by three different companies. It's the exact same knife. It's just that each has a different Japanese engraving on it, likely for the different company names. You'll find the design sold under three different labels Ryusen Damascus, Hattori HD and Maruyoshi HD. The Gyuto blade design is very similar to the Western Chef/Cooks knife. The main difference is that it has a thinner blade, allowing you to slice through food easier. And it also has a sharper cut angle. The knives are perfectly balanced. They are lighter than a Shun, Wusthof or Henckels. And they cut better than any knife I've ever used. Before, I never really liked to use a really long knife. An 8" chef's knife was my fave. However, I've found that their 300MM Gyuto design is very comfortable at even nearly 12" long. On the other hand a 10" Henckels feels as odd as can be in my hand because it is not balanced and designed properly.
One of the ways I get a good test on my knives is to properly cut up an onion. Cut off the tip and leave the root end on. Place the flat cut off end on the board and cut the onion in half right through the middle of the root end. Peel it. Bring the onion near the edge of the cutting board/counter. Then make the horizontal slices by rotating the knife from about a 30 degree angle to a 0 degree angle as you pull the knife towards you. The knife should cut all the way to the root end in one pull/slice. If it doesn't then the knife is either not sharp enough or the blade is too thick. You shouldn't have to try sawing through the onion on the horizontal slices. Finish the rest of the horizontal slices. Then do the vertical slices from the root to tip of the onion. The tip of the knife should easily chop down into the onion. If it doesn't, the tip is either not sharp enough or too thick. Then lastly the knife should make easy vertical dice cuts without pushing the onion apart. If it pushes the onion apart then the knife edge is too dull. The RyuSen/Maruyoshi/Hattori knife does all of those amazingly well.
It's one thing to have a knife with a sharp edge like a Shun. But after you use a sharp and well designed knife like a Maruyoshi then you're hooked and you realize the flaws of so many other knives. A good knife makes prep work go so much easier and faster. The other thing about the Maruyoshi knives is that they are about right at the same price point as a Shun, Wusthof or Henckels knife.
With knives it is very important to go with quality instead of buying a cheap set. Otherwise you'll likely find yourself buying better knives later, especially if you try out and find out what a good knife should be like. Two knives will do the mainstay of your work (an 8-10" Chef/Cook's knife and a 3 1/2" to 4" inch paring knife). Most like an 8 inch for a chef's knife and a 4 inch for a paring knife. Longer chef knives over 8" seem unwieldly like a sword for many people. And a shorter 3"-3 1/2" paring knife makes it harder to cut up stuff like an apple than a 4 inch paring knife. The extra length helps.