I'll go ahead and mention that you can get a lot out of the drawing by itself, regardless of how you handle the effects -- if you draw the hair lank against the head and a coat that looks heavy and dripping, then you can do the bare minimum of effects and still get the feeling of rain.
A rainy day from my comic:
there is a rain effect over everything, but it's literally just a ton of low opacity brush strokes (that I copied and pasted a bunch so I didn't have to kill my hand). What actually sells it as more than a simple effects layer imo is the drops splashing and dripping, and the fact that their hair looks wet
On the opposite end of the spectrum, you can get a LOT out of lighting and style:
https://tapastic.com/episode/224938
These are pages from noctuidae's Rainy Day, where the rain is stylised, minimal, and often simply implied... it's the atmosphere that really sells it. This isn't just rain, it's the feeling of rain -- a dreary lack of sun and light. I'd really recommend checking this one out, since the rain is portrayed in different ways throughout the comic -- some of them don't even bother to represent it realistically, with simple drop-shapes at the window, but again, it's the lighting and atmosphere that sell it anyway.
