What type of arduino do you use with Pd, and why? Just curious.

I mainly use the Teensy board as it is much more powerful than the Arduino. Lately I've been using this external ADC with this voltage reference for pots to raise the resolution to 16-bits.
Other than that, whatever fits the needs of each project. Arduino UNO is great for fast prototyping as it offers female headers.

I've used the MKR1000 to interact with Pd using OSC or FUDI over UDP/WiFi. For serial over USB, any old Arduino will do I think, but I've mostly used Mega 2560s for their extra I/O pins. I've only done one prototype with TCP/Ethernet and for that I used an Uno with a knockoff Ethernet shield. And for MIDI over USB, I don't remember what I used but it has to be one with a native USB port if you want it to look like a MIDI device when you plug it in. (Edit: I used a MKR Zero for MIDI/USB)

@alexandros how do you use this? For i/o audio, (as an audio interface?) or very high resolution analog control values?

Just high resolution analog values. If you want to do audio with the Teensy you need the audio board that's designed for this. But then it becomes rather independent from Pd.