Luggage advice for first time family flying please!

[LazyDoll]

Hi,
Having not left the UK for 11 years my family and I are taking a trip to the Arctic Circle early 2018 and I need to kit 5 of us out with new luggage!
I've checked baggage allowances etc but wondered if anyone travelling with children can recommend actual bags/cases or help more with sizes of luggage.
3 children 6/8/10 will definitely need luggage (they have back packs which I'm assuming will suffice for carry on) and us 2 adults.
Any advice would be greatly appreciated - thank you.

I take different shapes and sizes of bags for strategic car packing. Big case in boot, long thin one between kids, small ones at feet etc

Tie ribbons to case handles for identification