To get fast results I went the Wiznet way. There was already some software support, even sample projects were available for Raspberry Pico.

To me it was important to have a working software layer in C that would just work reliably. I tested everything was working by first connecting a Raspberry Pico to a Wiznet board with a W5500 chip. When I knew there were no issues, I designed the PCB.

I opted for the Wiznet W5500 because it would support 8 simultaneous connections (whereas the other variants didn't or were more expensive, e.g. W5100 only has 4 sockets). Additionally it would offload the RP2040 and its RAM having its own 32K buffer.

If you think about the different protocols involved: DHCP, DNS, SNTP, MQTT, HTTP ... and you don't want to reconfigure sockets all the time, then more sockets is  definitely better.