What is the best supported ethernet module for arduino

I would like to ask what ethernet library by extention the module, that is currently best supported? I would need this ethernet module to be able to support TCP and UDP at the same time.

UDP for the purpose of i can make the device be detectable by broadcasting techniques and TCP for the actuall transfering of data.

Im going to use the raspberry pi pico,

The best supported Ethernet chip in the Arduino world is the WizNet 5x00.

There isn't that much support for that platform in the Arduino world yet, so be cautious to only use libraries that doesn't include platform specific code.

I kinda like WizNet 5500 version.

but arduino has their own rp2040 nano which the pico also uses. so i guess it shouldnt be a problem, on top of that i have looked into wiznet5500 it uses SPI so there shouldnt be really any platform specific code.

I never said anything else. The Ethernet-Library should work. But you might do some other stuff on the board (other than networking) as this board is definitely not the best choice to implement a network only application.
The Arduino board using the RP2040 is quite new so not that many libraries already support that platform explicitly.