Sounds like a bad fuel pump or fuel filter. As already mentioned the fuel filter would be the first thing to try and replace. Its moderately simple and also cheep, i believe a new one is around $20.
I'm curious does it start on the second turn over or the second cycle. Try this next time, turn the key to on [but don't turn the engine over]. Wait a few seconds and then turn it off and on again. Now from the on position turn the engine over [push the key all the way forward to the ignition area]. Does it start right up?
