For commuting, assuming that you have a commute of more than 20 minutes, have to ride in traffic, and you have to leave the bike on a rack, I would say these are the must haves:
Spare tubes, patch kit, CO2 inflator and a few cartridges, multi-tool. Helmet, gloves, good cycling shorts. A high quality lock and chain. Lights front and rear. A ziplock bag for your phone if it rains. A floor pump for the home.
Other items you may want for comfort, safety, etc. as you do this more often; these can be pricey:
Fenders, saddle bags, a lightweight and breathable rain jacket, reflective clothing, over shorts to wear into the building, cycling pedals and shoes, a better saddle, thick bar tape, wipes (for when you don’t have a shower at the office), a place to put sweaty and smelly clothing that allows them to dry prior to your commute home, tubeless tires and sealant). If you’re parking in a risky area, a way to remove the seatpost and cover the hole. A bike computer for tracking your training, and possibly a Garmin Varia radar for traffic.