I don't ride much in the rain, I'm a slacker so don't cut rides short if it rains while I'm out but if I'm solo and it's raining before I head out I stick to Zwift. However...
From a riding point of view, watch for manhole covers or any ironwork, or any white lines, they can be really slippery. Also, try to avoid riding through standing water if you can't see the bottom, it can hide all manner of horrors.
From the kit side, mudguards, and a decent set of overshoes are key for me. Having wet feet, especially in cold weather, is horrid. I don't suffer from cold hands so don't worry about gloves too much. From a jacket point of view, it depends what you want to spend, and how far you're riding. I have a pretty cheap Pearl Izumi top that packs down small for a jersey pocket, which is adequate for the riding I do, but if I was riding regularly in the wet I'd be looking at the Gore Shakedry tops, or equivalent.