Living in Boston in Winter

Hi, I am 20F moving to Boston. As much as I am excited I am a bit cautious because I’ve never lived anywhere cold, let alone seen snow in my life. I am wondering what are some precautions I can take to be prepared for winter or at least things I should know. I am planning on moving somewhere that has transportation into Cambridge (where I’ll be working) because I do not want to bring my car. So im curious if winter storms impact public transportation and basic logistics like that. What are the worst months? Do markets close when it snows heavy? Do business cease during a winter storm? I just have no idea what to expect. I recently found out I may need to buy a shovel (?)