All you actually need is everything necessary to fix a flat on the road (which I say is tube, patches, pump and tools), vigilance and practice. Regular maintenance on the bike, the first step of which is checking before you leave: Air, brakes, cables, quick releases (abc-quick).

A rack is extremely convenient, or other more creative ways to get the backpack off your back. I'd recommend eye protection: sunglasses or goggles as you prefer.

Everything else mentioned here is good advice, in my opinion optional. I agree with not spending much money on equipment or clothes just yet; it's true that it can become a habit and get away from you. It can also be extremely cheap if you just refuse to buy anything unless you actually need it.

Beyond that, I'd just say be consistent with it. You might already be in great shape, or maybe you'll have to start slowly, but either way you'll improve quickly and it gets easier. If you keep at it. Eventually it's just easy, that 10 miles to work becomes routine.