Cleo, as long as your cameras all fit into a single carry on bag, you can usually take that on board over and above your usual carry on stuff. Some airlines get a little crappy, but when you explain to them that you are not going to check a bag (that now has to be unlocked) with $XX,XXX worth of camera gear, they usually get a little better about it.
My Canon XL-1 has a custom case made for it that fits all carry on spaces.
Lights, stands, whatever... you need a tough enough case that it isn't going to get killed on the way. However, as Torn mentioned, you will get killed if your baggage is over weight, and some will even ding you for a second or third bag these days.
If you know where you are going, it might be easier to send your stuff by courrier.
Alex