Necessities:

Water bottle and cage, 2 if you have the room (I don't on my small frame Giant and I really wish I did.)
Underseat bag to carry the following:
Spare tube, tire levers, possibly CO2 inflator, patch kit.
Frame mount tire pump.
Headlight if you ride in the dark or like me, ride in tunnels
Rear blinking light if you ride in the dark.
Cycle computer or cell phone mount

That gets you started.