Gloves are safety items. If you take a fall, they will protect the palms of your hand from a skinning. Essential in all conditions, but they also keep your hands warm in winter.
Basic puncture repair kit; carry it any time you dont want to walk back.
Are you using retaining pedals, toe clips or clipless. When you can ride and balance confidently, they will improve your safety and efficiency. Dont use clipless if you are still learning how to ride.
For commuting, fit fenders and a luggage rack. You need a bag to put your stuff in, a rack-top or single pannier bag will do the job better than a back pack.