Your question falls apart in several bits.
First of all, you can start your photo series at home, getting ready for the travel, getting packed, things loaded in the transport that gets you to the airport, the parts of the airport where you can take photos and so on.
You can take photos with other people in them, at least in Ireland and the UK, as long as you do not post them on open platforms. Sharing with people in a way that is not open is mostly not a problem, but if people see your camera (or phone or whatever) and show they do not want to be in the pic, respect that.
There are parts of airports where there are 'no photo' signs. This is to protect people working there and people passing through immigration and those parts of the airports, and you should always respect those signs.
Posting photos online, wherever and whenever taken, is getting more difficult over the years. What is allowed now may be illegal next month or next year.
To be on the safe side, do not post photos with people recognizable on internet unless you know the people and have asked permission to do so.
That way you will not break current and likely not break future laws. What is currently allowed differs per country and is subject to change, so I will not go into details. (See the comments on the other answer for details.)
If you feel the need to take a photo in the secure area of the airports, where there are usually 'no photo' signs, like to document something the officials there do, ask their permission and go by what they allow you. And if they tell you 'private use only' posting on internet is out of it.
In many parts of the airport you can take photos, it has been quite a time since I was in Dublin, but I have taken photos in many other airports and never had troubles finding ones that did not show forbidden subjects or recognizable people.