Puncture repair kit + tire levers. The most common thing to happen to bikes are having flat tires. Watch a quick Youtube video on how to fix flats.

Helmet. A must in the city. Like what the other Redditor said, just make sure they're not lemons, you don't need branded stuff.

A multi-tool. Allows you to tinker with just about everything on your bike, for when you start learning how to take care of your bicycle yourself.

Front and rear lights if you ride in the night. You can ditch the reflectors on the spokes, they barely help and they look tacky. If you're starting to get short on budget, buy a rear light first. IMO, it's more important for cars to see you than for you to see the road ahead, street lights and passing cars can help illuminate the way. You can do without a front light until you can afford one. For headlights, make sure to get directional models, and for rear lights, make sure it's not white and have flashing modes. I highly recommend the red Raypal Comet for taillights.