We've traveled from LAX to London, and it was likewise our first transatlantic flight (i.e., our first trip ever to Europe). What a wonderful trip it was, jetlag, cultural differences and pound-to-dollar shock and all!
That was some 40 countries ago, so indeed it all went well.
We picked up some prescription Ambien before our flight, and we took neck pillows along as well. The Ambien was very helpful, the neck pillows less so. Left them home after that flight (not to mention what a pain they are to deal with after landing and beginning our visit . . . ). We changed our watches to London time immediately upon boarding, and never allowed ourselves to do the 'well, it's only this time at home' thing. Just put your head in the time frame you are going, and eat and sleep as close too where you are going as possible. And try and walk around on the day of arrival, which is the only way were able to stay awake until the evening.
My preference for passing times on long flights is electronic jigsaw puzzles. DH's is Sudoku. YMMV.
Customs upon arrival is pretty much like customs here in the USA. Plan on a good hour in line, and be happy if it turns out to be less.
Taxis are readily available to get you into London, but oh boy, they are expensive. We took the Tube instead, even though, yes, this was our first ever foreign visit, but it's London so you can read everything and ask for help if needed.
Also, London is uber, uber safe, so don't worry about feeling lost/confused. You are in a wonderful city, and you'll eventually figure it all out in a very safe environment.
Dress nicely, BTW. Meaning leave the loose jeans and American bright-white sneakers and fanny bags at home. London is similar to NYC dress, and then some. It's so much nicer to fit in when traveling IMHO, than to stick out like a sore thumb. And it shows respect for the place being visited, which goes a long way when you need help.
Enjoy the heck out of your trip; London is fabulous!
