I recommend buying the ticket on the airline website (or hold the fare if that is the option offered) when you see a price you can live with. If in the US, as of 2012 the airlines are required to refund without penalty if cancelation occurs within 24 hours of purchase and the travel involved is not within 7 days. Some airlines (I believe AA) allow passengers to hold a fare/reservation for 24 hours before ticketing as an alternative to the rule.

I suspect this may not apply to Priceline, which often deals with non-published fares.