I've been flying overseas w/the kids since they were babies. As to how your particular trip will go, it depends on the kid, the day, the seatmates, etc., etc. There are too many variables to have any sort of guarantee of a good trip!
Some of the things I did...
Pack a mixture of old and new when it comes to toys. The comfort object/lovey (if there is one) is a MUST! Sometimes kids want something familiar, especially in unfamiliar surroundings. The new items are great distractions, especially if doled out one by one.
Pack food for the wee one. Airplane food, when and if they serve it, may not be to anyone's liking. I packed things like cheerios, crackers, raisins, etc. Also a no-spill sippy. Something to suck on during take-off and especially landing, as tiny little ears don't always like pressure changes.
If you can, make sure the little one has his/her own seat. It's not so bad from Newark direct to Edinburgh, but it's still an awful long time to have a 'lap-rider', both for the kid and the parents.
On most of the flights I took when my kids were babies, the crew was quite happy to help out with things like warming bottles, etc. On one flight, one of the stewardesses asked to hold dd....I didn't see her again for AGES! Turned out she got to spend most of the flight in first class. Once we'd landed and were waiting for our luggage, the first class passengers were greeting her by name!
Don't be afraid to take the little one for a 'stroll' around the cabin. It's a good excuse to stretch your legs as well. Helps get some of the wiggles out!
Be sure to bring enough diapers to get you through, then pack a few more. Plenty of diaper wipes to clean sticky fingers/tray tables/chair arms/etc. Also be sure to bring a change of clothes for the little one, plus at least a clean shirt for yourself.
Finally, most travellers have been there, done that. If things don't go quite as smoothly as you'd hoped, the flight will eventually come to an end...