We use alicante airport all the time as it is cheapest from Edinburgh. Couple of things too look out for
When exiting the airport make sure you take the road to murcia - its very easy to end up going the wrong way. Basically you either if you are exiting the public car park through the barriers it is straight a head of you rather than taking the bend round where the new terminal is bening built. If its form the hire car car park you head down and join the main road and turn left. Again it is straight ahead. its worth a look on google earth to see what I mean.
The car hire is is two places really, the first are in the terminal - record, avis and a few others i can't remember are all at the very end of terminal 1. go as far as you can and down stairs (towards domestic arrivals basically) the car hire desks are tucked in behind a cafe bit.
The other place is over in the car park itself. There a couple of vans in the public car park where hire companies work out of. I've used thes and they are fine. Just go over to the public car park opposite treminal 1. On your pick up instructions is should tell you were to collect from - mine was the second level but I've seen some on the ground as well.
there are some good insturctions that were previously posted on how to get to condado - i followed them and managed no proble. Just look out for the huge yellow sign with arabic writing on it once you pass the football stadium to make sure you get the right turn off then later on the one for bahia mazzaron for the next turn.
Takes me just over an hour to drive down usually in the smallest car the hire companies do - last time a picante - so small that i struggled to get the luggage and stuff we bought at primark on the way down.
That's another tip - it is worth stopping at the neuve condominum shopping centre as you pass if you need stuff for the house. I'm sure you've been before but we're still finding things to buy each time we pass - and as we don't have primark in edinburgh i have been known to buy stuff to bring back with me!!
If i can find the post with the airport directions on it I'll add it on here later.
Pamela Edinburgh and N4