As far as lights go, a really nice option which is highly reviewed with a very bright beam due to being an aimed beam, like a car headlight, instead of the standard flashlight type of lights, and the battery lasts a long time and is user replaceable, is the Raveman PR1200, it's only $90. Keep in mind you rarely if ever need 1,200 lumens on the road, heck cars only use 700 lumens on the road and they go faster than bikes do, so all you need to use is the middle setting which is 600 lumens...plenty for a slower moving bicycle. It's nice to have the 1,200 lumen capability because on a dark rainy night you might need the extra power. I do not own this light but I own something similar called the Phillips Saferide 80, it's designed with the same automotive cutoff beam as the Raveman but with a single LED.
Tail light wise, I own a NiteRider Omega 300, this is the best rear light I've ever found, it puts out an amazing 300 lumens which is extremely bright even in broad daylight. It has very good side visibility as well.
As far as other things, bike seat bag, I prefer Topeak Aero Wedge, but I did find a really inexpensive one made by BV on Amazon that is made of the exact same materials as the Topeak for a lot less money. Either you have to choose a size, first time bag, it's better to error on the size of large, by the time you put in a flat repair kit, levers, tube, mini tool, energy bar you'll be glad you got the larger one. Speaking of mini tools, if you're not real proficient at mechanical repairs then don't get one of those 20 or more some odd tool jobs, all you might need is some real basic tool.
Computer, just find one that has the features you want, they're all pretty decent these days. Wireless tend to have more reliability issues than a wired one and won't last half as long, but wireless look neater, but they also cost more.
People mentioned all the flat repair stuff, but the only mini pump I've used and really liked was the large size Lezyne Road Drive if you have a road bike, or the Alloy Drive if you have a bike with tires using less than 50 psi. Either of those can be had with a built in gauge. The Lezyne large road drive pump is the best mini on the market, it takes less strokes than any other and can get to over 100 psi; they make two shorter versions but keep in mind the shorter the pump the more strokes and the more effort is going to be needed. Best tire levers are either the Pedros or the Soma Steel Core levers, I have both and no issues with either, I've had the Soma for 13 years.
You'll need water bottle cages and bottles, lots of good cages just buy one that looks nice to you, I like some insulation in my bottles so I use Polar Bottles but I think Camelbak has better insulation.
Horn? or bell? no! why? because if you need a horn you probably need to stop, and using one hand to activate a warning instead of a brake doesn't make much sense to me, I would rather be stopping as fast as I can.