This list would evolved as you ride more and more. Most have been said, but I'll give you what I think it's important.
First, your not going any where if you don't have water. Camelback backpack or water bottle? I have tried them both and prefer water bottles, two better than one. You could get away with one if you pre hydrate before the ride and then don't go over an hour (depending on the heat).
Flats will let you stranded, sometimes in the middle of no where. I carry a spare tube, co2 bottle (if you don't go far from civilization, and pump if you do wonder, tire repair kit with glue less patches (glue patches are better but the glue dries out when you most need them). If you end up getting a pump, get one that inflates to 160 psi. Why? Because if you are out in the boonies and you finish changing a tire and now you need to get back home, you could get another flat (pinch flat) with a tire inflated only with one co2 cartridge. The need for a proper inflated tire, can only be archive IMO, with a pump rated no less than 160 psi (good to 110 psi) most of the pumps ratead to 120 psi are smaller and lighter, but would not pump passed 80 psi IMO (same as one shot of co2), that may or may not get you home.
With the repair kit, a simple multi tool. I had complex ones the end up doing work of simple work if you could of waited to go home and use the proper tool. I carry now a multi tool that adjust saddle, brake/derailure cables and tighten loose bottle cages carrier and stuff. Besides, they are lighter, and fit better on the saddle bag. Yes get a saddle bag! You will thank me latter. Nothing crazy, but one that carries the emergency repair kit. Leave the jersey pocket for food, wallet and phone. One that could fit a blinkie rear light on the rear would be nice.
One important thing to put in your emergency repair kit, MONEY, it has saved me from being stranded several times in my lifetime (54). I put enough to pay for a taxi back home or a LBS. For me that's' $50.00, if longer rides or touring then $100.00, and that's beside the wallet money for food and emergency repair at a LBS some where in the world!
Leave the computer for after you have some hours in the bike and you would know for what purpose you going to use the bike. If it's to stay fit or loose weight, a watch is all you need. If you want to learn how to ride efficiently as to go longer distance and touring and such then a computer with cadence. If your thinking of competing or even ride with other (it almost always ends up in some kind of competition) then I get one with heart rate monitor. If you think you ever enter competition, one the modern ones with Newton or watts consumption ($600 and up).
I ride day or night with rear and front lights most of the time. But that's because I live in a metro area. When I used to live in the country side I never worried before (but I was young and stupid). I would get good front and rear lights that can be used day and nights. With today LED advancement, this is possible. I have about $200.00 on front and rear, day/night battery lights. But that's just me!
if you ride in traffic, a rear view mirror is a saver for me. Tried many, settle on "Take a Look" glass mounted rear view mirror. Light, easy to adjust, handles vibration better than most and let you keep and eye on the rear traffic without constantly turning head or getting out of line. Takes a few rides to get use to it, but after you do, I don't leave home without it, like helmet.
Nice bike you got there, enjoy the ride and the journey. Bicycling is the only thing that have remain constant in my life. I thank God for the different places and all the joy it has brought me. I pray I can do it for many more years. Enjoy!
Double O