I find birding in the rain extremely difficult - even if your clothing is waterproof enough to keep you dry, the water on your optics (and in my case spectacles/glasses) severely affects the viewing experience. Fortunately, for most of my birding, there's little need to be out in the rain. That period before it rains, though, when it clouds over and birds start seeking shelter - that's often when things happen. Ditto when the rain begins to subside and birds start foraging again. That said, many birds will forage in drizzle and even light rain, and if you can observe from a sheltered position (or just stick it out in the rain) you may well be rewarded.
I'd say my favourite conditions for birding, here in London, would be with a moderate wind (say 10-18 mph) out of any westerly direction, bright, but with plenty of white cloud to silhouette soaring birds against. But every location is different, sometimes very much so.