Just riding around on the road? You don't really need lights, helmet, locks but they're nice to have. Essentially, the paraphernalia to fix a flat, water bottle and cage. The saddle bag is convenient, almost essential, for the tube, patches, tools etc because being attached to the bike you'll seldom forget them. I'd call the cell phone essential also. Strava app for the cell phone. Goggles, safety glasses or cycling sunglasses. MP3 player. Clothing accessories (jersey, gloves, shorts or bibs) are nice but also very optional.

For utility riding, and longer day trip type rides, you do need a lock. Some kind of bag to carry things, how to carry the bag is very much a personal preference. Commuting is a whole nuther story.