Since you want ESSENTIAL stuff, I'd suggest the following:

Spare tube + tire + tool kit + in a saddle bag
Frame pump
Lights + batteries
helmet
helmet mounted Mirror
bell / horn
a cheap bike
good locks
Rear rack + 1-2 bags for said rack
water bottle + cage

Tire Repair kit:
It's much better to have it and not need it, than need it and not have it. same with lights. One thing I would add is that you should practice removing and installing a new rear tube until you can do the whole process in about 5 minutes. My friend made this mistake and ended up having to flag someone down at because she had all of the tools, but none of the skill.

Helmet mounted mirror:
I've tried using handlebar mounts, but they require adjustment whenever you change your position or bump into em. I never wear a helmet, but I'm gonna buy one simply because it's safe in 2 ways (3 if you mount blinkers on your helmet)

Horn:
i've used bells before, and i have one on my bike for the trails and really cold winter riding, but if I'm doing some serious bike commuting on the busy roads at rush hour, I have an airzound bike horn. For those who don't know, it's an air horn you pump up using a regular bike pump, and blares out a 120 decibel honk with just a button press. If you're not interested in getting a fancy horn, at least get a cheap one. In the morning, you get people who are texting while blasting music with their windows up and don't hear you ringing your bell. A quick blast from the horn lets em know you mean business.

Cheap bike:
I know it seems like a terrible idea to put mileage on a cheap bike, but with some slicks, a bit of tuning, even the cheapest bike is ridable to work. If you can't get a cheap bike, I highly suggest that search your workplace for somewhere you could stash your bike indoors, just be careful that you don't track in dirt or leave puddles. If you would really wanna be on the safe side, buy a lock and at least lock the rear wheel to the rear triangle to prevent someone from rolling your bike out. if you're paranoid, lock it to something indoors like I do. A buddy of mine works half a block away from a police precinct and kindly asked the officers if he was allowed to lock his bike up in front and not have to worry about people stealing it.

Rear Racks:
backpacks are alright, but they make your back sweaty and gross. combined with sitting in an office chair all day might result in some serious BO by the end of the day. a great way to lessen this is to buy a messenger bag that can hang from a rear rack. Racks are also handy for all sorts of other stuff and definitely a must have for a commuter

Water bottles and cages:
Depending on your skill level you can have 1 or 2 water bottles mounted on your bike, but you should at least have one. Most people drink coffee first thing in the morning, and that makes you dehydrated. you might not notice it when you're at home, but as you ride you'll quickly find your tongue replaced with a desert and that can be easily fixed by taking a nice long swig at a red light

I think that covers everything, but I might be wrong.