You definitely want to get winter tires. They are more supple and wear out faster so take them off during mid spring to early fall. Depending on how long you plan to live here consider buying another set of rims so you can change them yourself. Then you just need a torque wrench and a jack stand.

Your commute does not sound like it would require chains. If you want to go to some remote areas outside the city, to go skiing for example you will almost certainly need chains.

Any decent tire place will do- just go for best reviews on yelp and nearest you. Best piece of car maintenance advice: check your fluids often and top them off or change when needed. This means oils, brake and radiator, (including making sure you have the right fluid with anti-freeze). Check tire pressure often. Temperature and altitude can affect it dramatically.

Good luck!