With the price of fuel what it is, and the state of a lot of the airlines, it's going to be hard to find a cheap, non-stop flight. You are best off deciding what you are willing to pay, then book the flight that comes closest to meeting your needs. The non-refundable flights will be the cheapest ones. If the fares go down after you have booked, most airlines will issue you a credit voucher, rather than an actual refund, but this will be after a 'flight change charge', which can differ from airline to airline.
Keep looking on the different airline sites and see what's out there. Then, make an informed choice.
