Bike, lock, and lights. I put lights above a helmet because "what if it gets dark?" seems to stop people a lot more than "what if I hit my head?" (and honestly, I consider that sensible... the worst bike accidents tend to be at night). The lock's price should go up with how difficult it would be for you to replace your bike. If you've got a $1000 bike and a minimum wage job... you want a damn good lock. If you've got a $50k/year job and no dependents and a vintage 3 speed that you saved from going to the dump, maybe the lock isn't so important. Same idea goes for lights. If you expect to ride a lot at night, you want good ones. If you expect they're for emergency use only, you can skimp.

In some states, gas stations are required to offer free air. In other states, it's customary. And then there's where I grew up, where it's 25-50 cents a pop... Scout around and find out which applies to you. Your tires will need to be checked for air at least once a week, and the higher pressure the tire the more often you should check. You can get by for quite a while off free air at gas stations. It is a good idea to have a floor pump and a portable pump, but that can easily run $70-80 to get both. Scout before you skimp tho, since tires that are low on pressure tend to get lots of flats. If you determine that you must get a pump right away, you can usually get a cheapie floor pump at Walmart or Target. The portable pump tends to be the really pricey one.

If you don't know how to change a flat, figure out how many bike shops are on your commute route. I remain firmly convinced that my bike knows when I've traveled out of comfortable walking distance to a bike shop. It is a very fretful bike and will have flats whenever we go too far from a bike shop. You can counter this natural bikeish tendency by learning to fix flats and carrying the tools, but flats are a part of biking. Again, this is an area where you can skimp, but scout so you have a plan first. I've often joked that my flat kit is my bus pass... but as I've gotten to be a stronger rider, I have gotten to the point where I might go out on a 20-30 mile loop of errands. Not all of those miles will be within reasonable distance of a bus stop.

As far as safety gear... you'll be the best judge of what you want/need. I'm pretty klutzy, as my collection of scars will show. But so far my worst biking injury was a badly sprained knee. I do wear a helmet, because as a klutz it is prudent. My head isn't very replaceable. But so far, neither head injuries nor scraped hands have been on the menu. If you know you're a klutz, you'll probably end up pretty injury free because you've got that voice in your head asking "and what happens when you screw up?" Think it over, take reasonable precautions, and you'll do fine. (the other voice, the one asking "what if THEY screw up?" you can't do so much about... a lot of the time you're more in danger from other people racing around like maniacs than you are from yourself. the best protection I'm aware of there is to never need to be a maniac. it's very freeing to realize you've got plenty of time and there's no rush and you can use your brakes liberally.)

And what caused my sprained knee? Wet railroad tracks. Certain kinds of falls on a bike are really common, and that's one of the common ones. I was lucky. The worst case scenario for that kind of fall is a spiral fracture of your femur. The stuff everyone is scared of, like getting hit from behind, is rare. Most bike crashes and falls are super predictable, and you can learn how to prevent them. That is 100% free, and absolutely worth doing. (naturally, most of my bike falls have been totally not common stuff... but the one common one was awfully dramatic.)