I use this guy (https://www.amazon.com/Tramontina-Professional-Nonstick-Restaurant-Aluminum/dp/B009HBKPD0/ref=sr_1_1?s=kitchen&ie=UTF8&qid=1487821426&sr=1-1&keywords=tramontina+8+inch+fry+pan) Costco has it in a set with the 12" one for $30.
These restaurant pans tend to last me 5 or 6 years.
Honestly speaking, I wouldn't just "buy a set of pans", I'd get them piece by piece by getting the ones I wanted on sale.
I also want to point out that true non-stick is the teflon-related coating, and they are temporary. They simply do not and cannot last. I've got a great quality teflon pan that is still doing great 5 years later, but that's because I treat it very very carefully.
For the non-stick frypan (the egg pan) I like either the 8 or 10" Tramontina. https://www.amazon.com/dp/B009HBKPD0/ These hit a great point between the $10 cheap shit and the $100 All-Clad expensive shit.
And... that's the only non-stick pan worth owning, because a little "sticking" is an important part of cooking (makes fond) so various levels of non-stick are preferred to allow a little stick.
I also use:
Those three you can get for cheap (if you're going lodge. The three above are like 30+60+15 --- about $100 in so far and we can already cook basically everything we need on a stove and all three are various levels of non-stick)
From here, things get pricier. We want to add stainless steel, and stainless steel is a lot more expensive to make pans out of than cast iron. A stainless steel fry pan (sticks more, but frys many things better) start at $50 for a good one. Tramontina from above makes an all-clad knock-off that's great.
Also want to consider the stainless steel sauce pans. Again, good ones run about $50/pan. All-Clad runs $100/pan. You'll probably want a small and a medium, or something like that.
From there you can just add a pan here or there when you find a deal or find something you truly need.
For $500 here’s what I’d get:
enameled cast iron dutch oven $80:
https://www.lodgecastiron.com/product/enameled-dutch-oven?sku=EC6D33
8 inch non stick fry pan $25:
https://www.amazon.com/dp/B009HBKPD0
12 inch stainless steel skillet $130:
https://www.amazon.com/dp/B00FUF5K8W
12 quart stock pot $60:
https://www.amazon.com/dp/B01M7RNBZA
3 quart pot $50:
https://www.amazon.com/dp/B00JAQ5NC0
2 quart pot $35:
https://www.amazon.com/dp/B00JAQ4DNU
12 inch carbon steel skillet $90:
That covers almost everything. A lot of people recommend cast iron skillets over carbon steel but I use my carbon steel way more because it’s lighter and easier to handle. I don’t notice any difference in cooking performance between the two and care and maintenance is the same.
For $500 here’s what I’d get:
enameled cast iron dutch oven $80:
https://www.lodgecastiron.com/product/enameled-dutch-oven?sku=EC6D33
8 inch non stick fry pan $25:
12 inch stainless steel skillet $130:
https://www.amazon.com/dp/B00FUF5K8W
12 quart stock pot $60:
https://www.amazon.com/dp/B01M7RNBZA
3 quart pot $50:
https://www.amazon.com/dp/B00JAQ5NC0
2 quart pot $35:
https://www.amazon.com/dp/B00JAQ4DNU/ref=cm_sw_r_cp_api_glt_fabc_G8DTZ5QM2XYJVFGEGJP0?psc=1
12 inch carbon steel skillet $90:
That covers almost everything. A lot of people recommend cast iron skillets over carbon steel but I use my carbon steel way more because it’s lighter and easier to handle. I don’t notice any difference in cooking performance between the two and care and maintenance is the same.