BMX bikes are not ideal. Why? No gears and it has a small chain ring, could be uncomfortable, and isn't very versatile.
I recommend a Hybrid bike. A combination between a road bikes 700c skinny tires but with an upright comfortable position. This allows a more faster ride than a mountain bikes fatter tires where you gain alot of rolling resistance. (Not good for city use)
Go to a local bike shop and ask about their Hybrid bikes. Get fitted. Fit is a important part of riding a bike. Without fit, you will loose efficiency. Shops will have all sorts of price ranges for every type of bikes. So go check them out.