Keep an extra full set of clothes at work since you have a locker, even if you're carrying clothes with you. That way you're covered no matter what happens, and you can try riding in work clothes if you want.

The challenge isn't in the equipment, as long as you have something reliable, so don't worry about that. Or about accessories. I have all of those mentioned - it's a hobby - but honestly half of my commutes in the summer are on a cheap bike, with no lights, no rack, no accessories, no hi-viz anything and wearing whatever was on top in the drawer. They are all good to have, but optional. Just get started.