Essentials:
Cycling is a very equipment heavy recreational activity. If you don't have them already, these are items that you should probably start with. The second set of items, although nice to have, are probably better to get after you've gone a few rounds on your bike.
How would you bike without one?
Probably the second most important thing to buy. It saves lives.
Keep yourself well hydrated, even if you feel like you might not need it.
It's always good to have your tires inflated just right.
You never know when you're going to need to make a small repair.
Nice to Have:
After long rides, these will help prevent blisters from forming.
Gym clothes works to start. Many of these items will improve comfort.
Very useful in metropolitan areas.
Useful and, in some cases, required to ride your bike at night.
Great, especially if you're using the bike to commute.
Your rear will thank you later.
Regular maintenance of your bike will help keep it going.