Just do it! YOU will be the best gauge of what you are missing (if anything) and can make tweaks to your own set up to improve your comfort. Your equipment may also change as your commuting expands - if initially you are doing fair weather and daylight only you'll need less than if you are riding in sub-freezing weather and heavy rains.

The only things you NEED are a safe bike (e.g. working brakes, no loose parts going to fall off) with air in the tires, and a good attitude.

If you are going to be commuting at all when it is dark, then your local law probably requires a front and rear light, and I would not recommend riding without them.

If you cannot bring your bike inside at work, you'll likely want to pick up a lock appropriate to the theft risk of the area you are going to be riding in. In some places any lock will do - just something to keep the honest people honest, for most places a u-lock would be recommended, and for high risk places (usually in major urban cores) you are best off with something heavy duty.

There are a myriad of ways to carry things by bike and you'll probably figure out what works best for you as you go. Depends on if you are bringing much to work or not - for instance if you plan on changing your clothes how are you getting them there? Backpack? Pannier on a rack? Leave them at work on days you drive?