My kids have been on long plane rides a few times and they handle really well. The first time my son was 4 and my daughter was 6 and we went to Italy. I was a little hesitant but they were troopers. They are now 11 and 13 and still do very well on long flights.
My best advice is to take the latest possible flight, if it is a non stop, so that by the time they settle in it will be their bed time and they will sleep for most of it. This has always worked for my kids
I also take hand held games, gameboys, etc, now they have ipods so I take those. Books to read, deck of cards or anything that will hold their interest. My kids school has a summer reading program that they have do complete before the following school year begins and I purchase their books and they take those to read on the plane, while in the room getting ready, etc
I always handled jet lag pretty good until I had kids but I think that has to do with worrying that they are going to be ok and I can't rest. The best advise I can give you is to try and sleep on the plane and don't go to sleep when you arrive but instead at your normal bedtime or close to it. If you cannot sleep on the plane, take a small nap but make sure you set an alarm because if you sleep too long it will totally throw off your internal clock
Avoid drinking caffeinated drinks or alcholic drinks on the plane this prolongs your jet lag.
Have a great time