I GOT THIS from an actor on a different site, Great info for all of Hey Jerry, congrats on the gig!
Advice from a million mile flyer...
Wear compression socks (aka Flight Socks). Dr. Scholls makes them. Continue to wear them for a few hours after landing until your body adjusts.
Bring a small flat pillow, a curved neck pillow, and eyeshades. (I would say earplugs but you can just dial down!)
Eat light before and during the flight, hydrate well, and avoid carbonated beverages.
Avoid sedatives, but do try to sleep on the plane if you can. When you arrive, get on the sleep schedule of that timezone. Maybe one small nap the first day, but the quicker you put yourself in the local timezone, the less jetlag you'll ultimately have.
Lufthansa is a good airline, very efficient. They're 100% partners with United Air Lines. If you have a United Mileage Plus account (and if you don't, then get one!), be sure to put your MP number on your itinerary so you can use the miles here on UA.
Be super nice when checking in and at the gate. Random free upgrades DO happen.
Can't wait to hear all about it!us.