If you must have stainless then look at the Kirkland set at Costco. Nice set for a fair price.
I would actually suggest mixing skillets and pans with DeBuyer Mineral Steel pans.
and then Le Creuset pots.

These are lifetime and cook better and clean easier than the stainless.

Mineral steel...what is that? Is it non-reactive?

It is just raw steel. With time, it develops a non-stick seasoning very similar to that of a cast-iron pan. It is not totally non-reactive, but a well-seasoned pan is pretty close to it.

Angie is correct.
Once seasoned they are pretty much as non stick as the best non stick pan once that non stick pan is 1 year old.
The Debuyer only gets better with age though while the non stick pan is usually toast and ready to be tossed within 5 years.
They can be super heated to really sear nicely.
Once well seasoned they are pretty much non reactive to anything short of doing an all day Sketti sauce.
But that is what the Le Creuset is for.

The Mineral Steel does everything the stainless steel does PLUS will become totally non stick, something stainless will never be.
They are also not expensive at all, less than most any stainless and are lifetime pans.
In fact if you have children they will use them until they are old and pass them to their children.
And they will work better 100 years from now than they do today.
Le Cresuet if properly taken care of should at least last your lifetime also.
Those ARE expensive though.

But you only need about 3 of those pots.

One 2 1/2qt multipot one 3 3/4Qt multi pot.
and one 8qt oval dutch oven.

I actually bought a 8Qt Kirkland Oval Dutch Oven which so far seems to be very nice.
Cost on that was just $79 Vs about $400 for the Le Cresuet.
The Multipots are about $170 for the 2 1/2 Qt

http://www.surlatable.com/product/PRO-1035534/Le-Creuset-Cherry-Two-in-One-Pan

The 3 3/4Qt is about $200

http://cookware.lecreuset.com/cookware/product_3-3%2F4-qt.-Multi-function-Pan_10151_-1_20002_41069_

The multipots have the added advantage of the lids being an 8" and 10" Le Cresuet frying pan.

Here is a link that might be useful: DeBuyer

I should add that you don't need to buy a DeBuyer pan to get carbon steel. I have one Paderno and one Vollrath, which are significantly cheaper than DeBuyer. Vollrath will be available at your local restaurant supply store. (DeBuyer has cachet among carbon-steel aficionados, much like Le Creuset has cachet among enameled cast-iron fans. But they work pretty much the same.)

The Vollrath is thinner, which gives it less searing capability and a bit less even heat, but it is a lot easier to move around.

Having typed all of this, I now realize your original question was more about pots! Ooops. Well, I will leave the info here for anyone who is interested.

Here is a link that might be useful: Vollrath pans from a restaurant supply store.

Dang that looks nice for $20.
Not familiar with these Vollrath pans but they look nice and for $20 how can you go wrong if they are even 1/2 as nice as the DeBuyer.
But they are considerably thinnner.
The Vollrath is just 16 gauge which is about 1.5 mm while the Debuyer is 3mm so its basically twice as thick.

True, it is considerably thinner. However, this can be an advantage! I have an elderly relative who loves cast iron, but is starting to have a hard time hefting it. I gave her a Vollrath carbon-steel pan, and she loves how light it is, yet behaves much like cast iron!

My Paderno is basically same thickness as DeBuyer.