Congratulations on discovering the most obvious secret of the universe. Don't tell anybody; you could cause the entire health care industry to collapse and bring on another Depression.

You've gotten plenty of good advice from the usual gang, here. A hybrid like yours is fine for commuting. Later on when you realize how much money you're saving you'll probably want to upgrade, but that can wait. Just make sure you carry tire-repair tools and know how to use them, plus perhaps a multi-tool with a chain tool incorporated. Being able to re-pin a broken chain and fix a flat will get you home 99% of the time.

Carry plenty of water, especially on the way home. Personally, I make my coffee and carry it into work in a stainless thermos that fits in a bottle cage, since one bottle is enough in the cool morning. I fill the empty thermos with cold spring water for the trip home, so halfway there I can refill my plastic water bottle with cold spring water.

Yes, and do that in advance. Are there other bike commuters in the company? What do they do? How you'll be storing your bike can have an effect on your choices of lighting systems, panniers, and other items you'd have to remove and reattach daily if locking the bike in an unprotected area.

Don't sweat it, though. You'll establish a routine and within days it will come naturally. Within weeks you'll be addicted.

The first time I did my current route (the same distance as yours) the big surprise was how easy it was. I felt almost embarrassed over how overprepared I was.

RichC