I bought a house with a pool, and we're setting up the terrace now. I want to buy armchairs and a small table to go with the pool. But I want to buy very nice chairs, not plastic ones and not cheap.

You should then understand that it will not be cheap. Cause high-quality furniture has always been pretty expensive. We bought a modern outdoor armchair https://www.roomservice360.com/modern-outdoor-furniture/chairs.html in this furniture store. The pieces of furniture there are made by Italian designers and manufacturers. There are beautiful works by Piero Lissoni, like neat chairs. But immediately after the swimming pool don't sit in such chairs, as they have a soft lining. I would advise buying two options.