For that kind of commute you don't need specialist cycle clothing.
I usually raid Go-Outdoors for generic hiking gear: polycotton hiking trousers or shorts, wicking Tshirt, light fleece pullover(s).
Your outer shell layer is critical, breathable waterproof for wet, more breathable windproof for dry.
W/p trousers are useful in cold rain and heavy rain but not warm summer rain.
Neck tubes, wool socks and decent gloves help in winter. Sealskinz or w/p footwear are useful. Sleeveles fleece gillet is useful for extra insulation under or over shell.