My suggestions:

Helmet - I never go out without mine.
Bottle cage + bottle (maybe x2, depending on how far you're expecting to ride and in what conditions)
Basic toolkit (a multitool will work just fine)
Tyre levers, spare inner tube or puncture patch kit, pump (listed on one line as if you don't have them all the ones you do have are useless in isolation)
Saddle bag (useful for storing the above, as well as some food for longer rides)
Lights (if there's any chance you'll be out after dark)

Other stuff that can be useful but isn't necessary:

Some form of eyewear to keep bugs out of your eyes
Cycling computer / GPS
Additional storage (rack and panniers don't leave your back sweaty like a backpack does)

Then over time you'll probably want to add things like cycling clothing - shorts, jerseys, shoes etc.