One of the most important considerations when planning how to travel with your equipment is figuring out what is mission-critical, and then making that your carry-on, when possible. I typically travel with a pelican case and camera backpack that fits under the seat. In these two carry-ons, I fit all the things that are critical for me getting the job done, and anything expensive or fragile. If a checked bag gets lost or damaged, I can still pull off the job. For bigger items, that's’ not always possible, but do what you can.
For other items, I check a large hard-case that has my drone and miscellaneous things like lights, audio equipment, etc. Invest in a good solid case that can hold up to the abuse of the baggage system, ask the airline for several fragile stickers, and hope that the baggage handlers are gentle.
Figure in the cost of bags for each airline when you’re looking at fares. Some charge painfully high fees for bags, especially if they’re overweight. Also ask your airline about their media rates, which you should be eligible for with a media ID card or business card. I found this article a long time back with an awesome template you can use to make your own media ID badge. With mine, I’ve never had a problem at the check-in counter. These regulations do change, so be sure to check ahead of time with your airline. Delta recently changed their policy to require travelers to submit the requests well in advance and no longer do media rates at the counter.
Beyond the airline and their policies, when you fly internationally, you’ll need to research your destination country’s customs regulations. Find out if you need a work permit and if you need to get a Carnet to avoid getting charged an import tax.
One of the best things I started doing last year with travel was using LensRentals.com to ship in equipment. They have a huge inventory of rentable equipment, and they’ll ship it to you anywhere in the US. The prices are reasonable and they have a yearly membership for free shipping, which is definitely worth the $99 if you plan on doing a few orders.
I’ll have them ship in the bigger things like tripods, lights, extra camerasm, etc, and have it delivered to a FedEx store near my hotel to be held for pickup. When you’re done, you box it back up and drop it off on your way to the airport. Pretty easy, right?