Yes, you need a helmet. Your new bike is more of an off-road/commuter hybrid and it has wider tires which may require some adjustments to the brake levers or shifters but if this doesn’t sound like something you’re interested in then we recommend getting a modern road bike instead.
If your interests are solely on using the bike for commuting (or riding around town), then congratulations! You’ll be able to go pretty much anywhere with ease just make sure not to wear any clothes that will get caught up in your chain. We also recommend a bottle cage mount so you can carry water with you when gearing up for those longer rides; there’s nothing worse than being out on the open road without enough water available.