Hello Mrs Dobby, how wise you are to go for top quality pots. Your investment will bw well repayed.
In relation to pots I would say it's horses for courses. I wouldn't (didn't) go for a matched set. Work out what you need and what you want each pot to do for you.
I see no need for a non stick pot to make soup, boil vegetables or potatoes. For these purposes I bought stainless pots with copper bottoms. Meyer Copperal range. I've had them 20+ years, find them excellent, look like brand new, and completely dish washer safe. Can't recommend them highly enough.

For non stick pots, for frying, browning meat, making sauces and slow cooked stews, I have several in the Circulon range. Had them 10+ years and they're like brand new. Highly recommended. They say thay are dishwaher safe but in honesty, they are so easy to clean I rarely put them there, but they have been in with no ill effects.

These ranges can be very expensive in the big department stores. I bought mine for quite reasonable prices (less than half price) in our local Co-op kitchen department.

Wharever you decide to buy, shop around for the price. You'll be amazed at the differences. Good luck and let us know what you decide to go for and how you get on.