Andrew, if you've got a few weeks until you fly out, you might as well start now. You'll be used to it well before then, and a couple of days' change won't hurt anything long-term. You can't really mess anything up.
On the getting to sleep thing, I used to be the same. In my case the answer was just to write a to-do list (with everything that was on my mind) each night before bed. Beside each item there'd be a quick note of the action I was intending to take - even that was 'unknown'. I was able to stop thinking about everything then, knowing it had been taken care of until the next day.
Something else to look at is your diet; I'm sure you're not having several cups of coffee or anything just before trying to sleep, but there may be something else. A large meal of something which takes a long time to digest for example.
With the weights, what's your main goal? Strength, hypertrophy, training for a particular sport etc? It's definitely strength in my case, and the hypertrophy is just a nice benefit