European carry-on rules are slightly smaller typically than what US airlines allow, so check the fine print on the airline websites. Also, US airlines tend to be by item, not weight - two bags or whatever. In Europe, the weight is much more closely monitored typically - even for carry on. It depends on the airline how closely these are policed, but the last thing you want is to be forced to put L lenses into the hold... My experience with Swiss and Lufthansa is that they are fairly relaxed about carry on. I generally have a small Kata camera backpack, and a smaller Kata bag, all of which stack together onto a system trolley which is just about within carry on limits, at least size wise. Then when I get on board, I put the camera bag in the overhead rack, and the smaller bag into my lap with magazines, ipods, etc. And if someone gets difficult, you can split the combo into three - foldable trolley (into the hold worst case scenario), camera bag on your back, and small bag.
You shouldn't need to carry receipts, though if it worries you, perhaps you should. With (presumably) a US passport, the serial numbers would in any case trace to US purchase, so even if push comes to shove you should be OK. I've travelled very widely (I work in technical sales) and I've NEVER been stopped in regard to equipment, either in the USA, Europe or indeed anywhere else, but there are no guarantees. Customs are looking for dodgy drug dealers and cigarette smugglers, not honest tourists with cameras, as a rule. They are looking for things which are 'out of whack' - someone with no camera body but lots of lenses, for example. Bear in mind that no one (apart from US immigration it seems) are trying to turn away honest tourists.
Tripods - no use if it isn't with you, so pick something light and portable. The Gitzo traveller range are superb, if expensive.
One important point: NO FLUIDS in Europe in carry on. So don't pack bottles of water, and anything you buy in the airport will probably have to be abandoned at some point. Switzerland is not in Europe (well, the EU), so the rules are a bit different, for example on customs restrictions and allowances.
Have a great time, and don't tip what you usually do - Europe is half of what USA tips, as a rule. (10% not 20%) - even less in Switzerland.