Hi Liz and welcome to the forum!
In my personal opinion, I would book your apartment first as some airlines don't release their flight schedules until later in the year, sometimes not until after Christmas (in our case, Easyjet from Luton).
We booked our villa last year in November and the original dates we wanted had already gone so it's worth bearing this in mind.
We didn't wait around for Easyjet and booked through Air Berlin a few weeks later. There was no problem booking seats in the summer holidays.
This is just my personal opinion, Liz, but others may disagree so at the end of the day it's really down to what apartments are available for the dates you want. If they're available, grab them quick!
Good luck!
Jane