If your ESP is relatively close to the rain collector, I would suggest you don’t need any further filtering. I put a 'scope on the rain collector and the anemometer to see what sort of waveform they produced when they “pulsed” and it was extremely clean out of the box. If you have to run your cable from the collector to the ESP past a lot of noise (such as electrical wiring etc.) as I had to, then perhaps it is worth adding a filter.
The Pro mini I’m running is also at 3.3V but I’ll have to climb into my roof space to see what RC values I used. I’ll try and get up there tonight when it has cooled down a bit. This time I’ll write them down!
[EDIT]
I should have warned you that the rain collector is MUCH larger than the cheaper ones that provide 0.5mm / tip. Expect a reasonable sized box to turn up!