I was worried about those same 2 things before I went abroad for the first time last December.
RE: No Jet Lag as mentioned by Ken.
I have used it for both trips to London and I have to say, after the first day and a good nights rest, I am usually on target the next morning. Up and out the door by 9 am to sightsee. I havent tried travelling without it so I am not sure if it is a placebo effect or not, but since one package gives you enough for a few flights (i dont use it on the way home), its worth the $10 to give it a shot. I doubt it can cause much harm. They sell it at Magellans, some Whole Foods and most Travel or Luggage stores.
I was also worried about the Deep Vein Thrombosis after reading some of the stuff here. I am a "larger" woman and after 2 international trips, I have yet to have any issues with that. Just move your legs alot and stand up every chance you get.
Though after my last trip home, my feet did swell for 2 days, which is unusual or me, but that went away after I elevated them. I believe that was because on my first trip I took connecting flights, so I walked in the airport. The second trip were non stop flights, so I was sat for almost 10 hours!!