Recommended check-in time for all flights is 2 hours before departure, but if the airport is not busy (it rarely is) you can risk cutting it to 90 or even 75 minutes.
Before today's fuel cost increase a taxi from Amman to the airport cost JD 10 for locals. A few days ago I was even offered a ride from the 7th Circle to the airport for JD 5, but I suspect the driver (though keen for a job) would have tried to renegotiate for a generous "tip" en route. Foreigners are asked JD 20, but drivers will quickly settle on JD 15. This is still too much, so bargain down to 12 or 13. (The metered fare would be JD 7 or 8.) Be prepared to tell several drivers to go to hell, then try the next car. At busy times you often have 5 or 10 taxis available within 50 metres around you, so you do have some bargaining power.
If any driver uses the new fuel costs to justify a price increase by 50 or 100% he is ripping you off. 10% to 20% more would be be reasonable. The government has authorized a price increase of 10% for "official" taxi fares FROM the airport, but these are already inflated (JD 17.500), so they can absorb the higher fuel costs more easily.

