This is in order of importance, in my opinion of course.
First thing you should consider is whether or not you need your brains, if you've said yes than get a helmet.
The second thing you need to learn, if you haven't learn how already and that is to know how to fix a flat. There are lots of Youtube videos you can watch to learn then simply practice, especially on the rear tire so you can learn how to deal with the mechanicals because rear flats will represent about 99% of your flats, so you better learn how to deal with the rear.
Third thing you need to know about is pumps, very few pumps will get you 100 psi, most will get you to about 75 regardless of their lofty claims they put on their packaging. Buying a cheap pump won't last you very long and nothing will be more frustrating than going on a long ride and have flat then the pump fails. The only pump that I would recommend is the Lezyne Road Drive large (they come in 3 sizes, small, medium and large, the large size is the easiest to use). Yes it cost more but it's built well and it will inflate to 100 psi in less strokes than the few others that will get that high. I don't care for CO2 unless your racing, CO2 cost money, CO2 gives you limited air supply, CO2 air bleeds through the tube a lot faster so you have to go home and drain the air all out and refill with normal air, I hate doing things twice, CO2 has waste that you have deal with of course some people just throw them on the side of the road...nice.
4th you need a seat bag, I've found the cheap BV bag that is made of the exact same materials that the Topeak seat bags are and they're very rugged. See:
https://www.amazon.com/dp/B00A3W8FFM?tag=dabestproducts-20&th=1&psc=1
5th you need a patch kit, glue on works really well, but I use Park and only Park glueless patches, they are the only ones that work, the rest only hold for 24 to 48 hours while the Park will last the life of the tube but they do require more attention to preparation that should also be done with glue on but if you mess a step with glue on you usually won't have a failure unlike glueless. If you decide to know about how to make glueless work reply back, I've been using them for over 20 years with only one failure because it was my first one and I didn't do it right. The patch kit also includes buying a pair of tire irons, wider tire irons work best for large tires like MTB tires, but for road tires you need narrower levers. Pedro levers are the best plastic ones, but the strongest is the Soma steel core, they cost more but will last forever, but the Pedros are strong too and will last a long time.
6th thing you need is a spare tube. I can fix a tube as fast as another person can replace it most of the time, so most of the time I fix it on the road, again I don't like doing things twice so it makes no sense for me to know where the hole is take it out, roll all the air out, get it home refind the hole and fix it, when I can avoid all of that and just fix it on the road. Even if it was faster to replace the tube on the road, I would still prefer to fix it first so I don't have to worry about it when I get home, again I'm not racing so I don't care. If you want to know how to fix a flat fast again let me know.
7th thing you need is water bottles and cages. you can get any water bottle, I happen to like Polar because I can make the drink stay colder longer. Cages again anything can work, for cheap but lightweight cages Bontrager RL cages fit that bill plus they're strong and will hold large Polar bottles with no problem.
8th thing needed is a tire boot patch from Park, these will get you home should you put a large gash in a tire, yes you can use a wrapper from a candy bar but those will simply rip when you run over some object just right that hits the wrapper, the boot patch is thick and highly resistant to penetration as well as the tube trying to push through it.
9th thing you need a sponge or two and some Dawn for Dishes, the non citrus version. Use one sponge to wash the bike with, and the other to wash the chain with. Do both at the same time, then rinse with a gentle spray of water the whole bike off. Dry the bike with a dry microfiber towel. Wash the sponges in a tub of water with Dawn for Dishes, and make sure you get all the soap out of them. After the chain has dried apply whatever lubricant you like, I'm pretty much sold on Rock & Roll lubes, just follow the directions on whatever lube bottle you buy. After you lube it you should let it dry for about 12 hours and then wipe the chain (Rock & Roll wants you to wipe it down immediately after you ran the chain a dozen times or so backwards), then after every ride you wipe the chain down. I use cheap bulk red towels for the wiping down process, once the rag gets too dirty to use I throw it away.
10th thing is IF you know how to work on your own bike to some degree then you should consider a multi tool to carry with you to do minor repairs. I happen to like the Park MTB 3.2 but again that's a personal choice, you have to decide how many tools you think you can use.
11th thing you need is a bright tail light, the best I've found for the money is this:
https://www.amazon.com/Lezyne-Zecto...H5&pd_rd_wg=4g6cd&refRID=KHTC1XB6VAJ2KX0DGV5Q While 250 lumens seems bright remember you should use this even in bright sunlight so it needs to bright enough to overwhelm the sun, plus it needs to be bright enough to be seen for a ways, and bright enough to attract the attention of that moron texting!
11th, headlight if you'll be riding in the dark, some say you should get one for the day so people can see it flashing, hmmm, that's an interesting thing since I can see better in front of me than behind me I can see who's coming at me, so I don't know where to rank this one, so I put here for fun. Headlights you need to get one that has at around 650 to 750 lumens on the middle setting, which means the high setting is used for dark rainy nights when about 700 won't be quite enough.
12th is a lock IF you plan on locking it somewhere, lots of locks on the market suffice it to say that cable locks are the easiest as is a new weird thing that looks likes a zip tie. The best for the money is this:
https://www.amazon.com/Kryptonite-K...=sporting-goods&ie=UTF8&qid=1403017184&sr=1-1 Of course there are better locks but they cost quite a bit more, and depending on the value of your bike would determine how much you should spend on a lock.
Those are the real necessities, all the other stuff you can add are not really necessary to start with and some I listed are optional depending on your needs. There is more you will over time add as you decide what you need. I didn't mention clothes because that's sort of obvious because it's illegal to ride a bike naked in public...