Caroline
I travel EasyJet quite a bit (infact my next flight will be in two weeks time).
In my experience I carry everything I need as hand luggage. I find although there are rules about what you can and cannot carry-on, not all airports do the same.
I have a Pelicase which takes 99% of my gear. What I cannot get in, I put into coat pockets. You are allowed one case up to a certain size (My pelicase is actually smaller than allowed) Technically you are not allowed any other bag, that includes the duty free you have just bought and at one european airport ladies were told that handbags were not accepted with another bag, they had to be put inside the ONE bag allowed.. But as said before, the good thing is that there is no weight limit.... Be aware, they will stop people that obviously have a bag that is bursting at the seams..
Another plus is that you are allowed a coat and it doesn't matter what you have in your pockets... So fill them!
You may or may not get away with carrying a tripod. For years, I used to carry a monopole, until I flew out of Frankfurt. Although Adolf said I could carry it on this occasion, next time he would not allow me to carry it! Could never understand why it was okay to take it into Frankfurt, but not OUT!
As for check-in luggage, Easyjet have now changed there booking-in procedure. You now queue up with every other EasyJet traveller, the people that are going to... Spain, Italy, France, Sweden infact anywhere.. One big long queue. So you could be queing behind someone that has a later flight than you. If you need to book in luggage, get there early.
What ever, enjoy your trip.
BTW, Easyjet is far better than the Irish airline..