Hey Brooke,
I;m going to go through what you have said point by point so that all is clear:
first of when is your flight landing? that might lessen the possibility of getting a city taxi rather than an ariport one.
1- there are airport taxis that you can book on arrival the prices are listed on a board, the phone number to call and confirm prices and times are Air Port Taxi Tel 00962 6 4451074 or 00962 6 4451302. Prices have changed since Fuel prices went up so i'd rather not stick to a price!
2- As people mentioned booking a taxi to the dead sea and back is not difficult is around 60 jds, and as other posts have mentioned you should probably book a room by now since Dead sea at this time is quite popular. if as you said price is not an issue book a room at the Kempinski its fantastic. All hotels have access to the sea.
oh and one more thing, there are several taxi offices around amman, get your hotel to suggest an office (DO NOT book Taxi Mumayaz, they are a nightmare to deal with) and arrange with the driver when to drop you and pic you up.
3- Everyone mentioned driving in Amman, now booking a car with GPS is less of a hassle and driving from amman to dead sea is easy as it is a straight road with lots of signs. Now I have a friend who came from UK and drove in Amman and to dead sea, she said she got lost in the streets in Amman, the reason would be is street names are confusing! even with Sat nav,
but in general you do not need a car if you want to tour Amman (its a small city and taxi;s are hassle free, be wary that taxi drivers will try to rip you off, the maximum fair if your moving in central amman is 2 Jordanian dinars!)
hope this helps! have a good time in Jordan :)
