no bad weather, only bad clothing.

motel style shower cap for over the helmet
cycling specific rain jacket not form fitting so you can move and wear other things underneath if necessary
cycling specific rain pants
yes, you may be wet from sweat but you need to protect from cold rain water
shoe protection, I used rubber overboots but that's me - big variety out there but you have to protect the shoes from getting wet
eye protection, yes the glasses will get wet and need to be wiped but there's all kinds of stuff flung up from wet car wheels and you don't that garbage in your eyes
strobes and reflectors front rear and sideways, when drivers vision is obstructed you still need to stand out, so wear bright colors
riding with slower congested rush hour traffic is safer than off hour faster traffic

good luck, and be safe

oh yeah, fenders! :-)