Was myself in Alic last may and flew out from there. There is a dependable city-bus type link to station, about ev 20/30 mins. Cheap, but not that fast.
As about everywhere in ESpana there is also a kind of expressbus (coach for most British) to the next major city, Vlc, but it varies by trip how it goes-the main motorway folllows th coast mostly and thus serves those overly famous seaside towns as Benidorm etc. and these will be served by that bus-if there are just a lot on that trip, it wont be fast. IF a train has just left and the wait is very long for next, you may want to consider that, but check first.
Check yourself if by now also FLIXbus has an offer, but do not book untill there and really sure you will use it.
For trains; there are likely also other types and prices vary by class and type of train, but if you do not ant to risk to pay for nothing (flight delay->train missed etc.) then you may, in current high season and more on busy weekends-days, get informed that ´vostre treno es completo!=train fully booked, as it all goes on reservations.