I have just returned from Fuerteventura and after trying the other canary Islands have to say Fuerteventura is my favourite.
Last trip stayed in Correlajo which is more commerical this time stayed in Calete de Fuste and loved it.
As mentioned by Cuchailinn the resort is quiet so you can walk in peace no one trying to sell time share, get you into restaurants etc.
There was a breeze but it was welcome, we were there in jan last time and weather was a nice 21-24 every day.
Fly with Ryan air (all 1c flights for Jan are now sold) but still not too expensive. Check out this web site for good deals
www.thomson.co.uk (prices are in stg) click on hotels= fuerteventura and your date you will get a list of available.
Jan 17-24 will cost 210 stg in a 1 bed apartment in the Castillo San Jorge which is a fantastic hotel overlooking the sea, it has a kiddy club, there is a promanade walk from it to beach 700 mtr and you can feed the chipmunks the twins will love them they are so friendly and will eat from you hand.
Hotel has 3 pools and 2 a la carte restaurants as well as buffet.
Taxi cost us 9.50 from airport.