Oh, wow. You're "new to commuting" and doing a 20-mile commute?
As for supplies, though I'm a novice at this too, I'd recommend a portable pump, patch kit or spare inner tube, multi-tool, water, maybe a change of clothes, locks, emergency cash, cellphone, and other stuff that doesn't come to mind right now. I recommend that you read through at least some of this whole thread starting from the beginning. There are lots of equipment mentioned by commuters at the first pages of this thread.