Welcome to the wonderful of commuting, here is what you'll need:
appropriate clothing for weather, leg warmers, arm warmers, beanie, helmet. Thats for Cold weather.
Warm; comfy shorts, knee warmers, arm warmers. Change of clothes if you have to change when you get to where you are going. Fenders if you ride in wet conditions, panniers? I dont know I have an Xtracycle and it makes life easy.
Need more specific info for more specific needs.
Good Luck
I commute year round and live in the mountains so I ride through single digits temps and foot deep snow.