Things I wouldn't be without on my commute (well, besides the bike!):
-spare tube (don't try to repair it until you're in the comfort of your own home. And check inside that tyre before you put that new tube in!!!)
-pump, puncture repair kit, tyre levers and a multi-tool.
-helmet (won't start a debate, but I have to have one on my commute into work as its mandated)
-helmet mirror
-high viz vest
-lights
-shoes (have spds)
-cycling shorts (fat thighs -a real necessity!)
-gloves (I wear full fingered all seasons, non-padded, just a personal preference)
And things I might not have but most usually do:
-zipties, electrical tape/duct tape, phone.
And now some less obvious stuff I do:
-I check to make sure I have what I think I have.
-Now and again, I check to make sure my pump works, and that I have glue that works with the patches.
-I always have 2 bikes in case one is out of commission
-I usually prepare the night before
-if I don't feel safe on the road at a certain place, I try to approach it differently, not necessarily cycling, or I avoid it altogether.
-if something isn't right and it's a new problem (e.g. brakes catching) I stop to make sure I know why.
And.... finally, I'd say learn bike maintenance -cheaper, faster, more convenient.