We booked
shuttle transfers from airport to Costa Teguise via EasyJet website, although we weren't flying with them - they act as agents for local transport companies. It was straightforward and listed the various options and prices.
Can't mind the exact fare - but it was quite reasonable, about 12 Euros each return, from memory.
When we got to Arrecife we were the only clients booked to transfer to CT - so they immediately laid on a coach for 2 passengers and there was very little delay - and no charge for luggage as taxis do.
We've also taken a taxi at the airport, the wait is not too long and fares reasonable.
One time we hired a car from the airport for the week -
that is well worth considering - it cost 100 Euros (we got a good late deal) and the return taxi fare was around 40 Euros - therefore we had the "extra" use of the vehicle all week for 60 Euros - and handed it back at the airport, no problems.