The following are the most important things for a commuter. In my opinion there is no ranking—they are in alphabetical order. I simply do not ride if I do not have these item properly checked off.
In the northwest the most common comfort issue is cold and rain. At times I feel I carry more clothes than work items. Gloves, warm-ups, over boots and jackets; I always seem to have an extra set.
I use booties for both warmth and to keep out water. They cover the vents in your shoes. I like the Sugio because they are easiest to get on and off. Many do not like their Velcro strap under the shoe, but I have fond no problem with it. That could be since I wear a mountain bike shoe with a lot of room for the strap under my arch.
I will have on my booties long before I put on my leg warm-ups.
Leg and arm warm ups are also essential. They reduce what you have to carry and you can wear them in the morning and not in the afternoon... or take them off mid-ride. That is a lot easier than finding a place to change and carrying that change of clothes.
Unfortunately I have not found a good solution for 30°F in the morning and 50°F in the evening. This almost always takes two jackets, a heavier, even insulated and a light vented. I simply carry two with me.
So much has been said about helmets that I can not add any more. Get a good one and wear it (WITH THE CHIN STRAP TIGHTENED)
I started using a mirror in 1978 on a trans-am ride and I have never stopped using one. I am sure that it has gotten me out of hundreds of pickles and kept me going straight. I really do not care how good a rider you are, if you turn your head/body to look behind you, your bike moves and all too often into the lane traffic you are trying to look at. Just the wrong thing.
I strongly recommend a helmet or glasses mount mirror, they are steadier and more versatile. A mirror, just like the one in your car, let's you stay aware of who is behind you. Once you are used to it (see below) you will find that you are less anxious and more comfortable riding. The area covered is similar to a car, by with the slightest movement of your head you can see anywhere.
From the front
Caution: A mirror takes some time to get used to. I have gotten them for my wife and kids and I have to tell them, "Don't forget to look where you are going!" Seriously, until the novelty wears off, people look in their mirror too much and don't watch where they are going.