A tired traveller... what to do?

I'm arriving in Frankfurt International at 8:30pm on Sunday the 9th of September (2007) and am trying to book a flight to Alicante either that night or the next day. I've been looking at Air Berlin. Coming from Perth it's a bit of a long haul and i'm looking at a few options.

Air Berlin don't have many available flights besides early the next morning (4:15 or 5:15am!) or the morning after (so Tuesday!). I was wondering if there was any other cheap, reliable airline that flies into Alicante from Frankfurt International and if i have to stay the night, what would be a good place? Any cheap airport hotels or secure hostels? Or should i risk the exhaustion and stay in the airport to wait for the flight?

Ideally i guess i would be looking to stay overnight somewhere then possibly fly out during the next day - Monday (afternoon to evening?).

Cheers.

Where are you planning to stay in Alicante? Because if convenient, you could fly on the monday at 13.50 to Murcia (1.3 hr south of Alicante the airport is actually closer to the coast than Murcia city) with ryanair for €24 or with ryanair to Valencia (2 hr north of Alicante)for about the same price. I cant find anything elso from frankfurt to Ali than air berlin.