One thing to keep in mind, it's totally illegal, and rightly so, to check lithium batteries in stowed baggage.
You can check lithium batteries if they're attached to something (i.e. installed in a device). Not sure why that's any safer than loose batteries.
When I was your age, we could carry on all sorts of gear — two or three bags of cameras/lenses and a large case of studio strobes. Back then, being a news photographer meant something.
There were a number of times I was able to walk around airport security simply because I was a news photographer and they felt I shouldn't have to wait in line. Also a number of times I was allowed to board first so that I could stow my camera gear.
In a couple of countries (Mexico, Dominican Republic), my local assistant drove me right up to the plane on the tarmac, completely avoiding the airport terminal, simply because I was a news photographer.
Could also ship film back to Canada for free.
Those were the good ol' days that ended around 2001.
I'm sure other photographers could astound you with stories of how great access was to almost anything simply because you were "the newspaper photographer."
I've checked gear in Pelican cases, aluminum cases and soft-sided Lightware cases. Always gave me extra stress as I worried if my gear would show up at the other end. Only twice did a case go slightly astray:
1) When a case didn't show up on a baggage carousel, after many panic-stricken minutes, by chance I glanced out a nearby window and saw my case sitting out on the tarmac all by itself. Apparently, it fell off the baggage-tractor-thing while being transported from plane to airport terminal.
2) After a case didn't show up on the baggage carousel at a US airport, I wandered around the empty arrivals area and found my case sitting all by itself in a far corner. No idea how it got there.
Once had a soft-sided case arrive soaking wet even though it wasn't raining outside. Water went though the case but the gear was okay.
I've known two photographers whose soft-sided Lowepro roller cases were crushed while in a plane's hold. Also, another photographer who had a camera stolen out of her checked bag presumably while it was passing through TSA security.
Domestic travel (not sure about US travel) — right after you book a ticket, call the airline and ask for special consideration for carry-on. Tell them that you're a professional photographer and will be carrying $35,000 worth of "digital equipment" and "special glass lenses". You really, really need to carry-on this "high value" equipment. Be sure to say that your bag(s) (don't say "case") will absolutely positively fit in the overhead bins (and make sure that they do fit). If they refuse, you can perhaps cancel your ticket right away without penalty and try another airline.
I've had Canadian airlines (WestJet, AirCan) put some sort of notice on my ticket allowing me to carry-on an extra bag and extra weight, providing space was available (i.e. not a full flight), and board first. But maybe I just have a nice telephone voice.
If an airline does give you extra carry-on, after your flight(s), be sure to send a thank-you to their PR or CEO. Let them know how wonderful their employees were and how much they helped you. Don't mention that you got extra carry-on or extra weight; just say their employees were so nice and helpful. Keep flying with them.
If an airline doesn't give you extra carry-on, get a couple of big, ol' camera bodies (e.g. Kodak DCS520/620), drive to the airline office and toss the cameras through the front windows.
I've found that an airline won't help until after you've bought a ticket. If you buy the cheapest ticket, there may be little incentive to give you any concessions. It may also help if you fly on the least popular flight (i.e. the one with the most empty seats) — often the first flight of the day. It also helps if you're a frequent flyer of that airline. Might also help if you're dressed nicely when you arrive at the airport.
I've also found that airlines care about baggage size first (must fit in the overhead) and weight second. Although, a current lawsuit against Air Canada, for a carry-on bag that fell from the overhead onto a passenger's head, may change airlines' attitudes about weight. Some airlines are more strict about size and weight because they can charge more fees.
Hard plastic cases (e.g. Nanuck and Pelican) now come in lighter-weight versions which will save a few pounds. Cases with handles and wheels are easier to manoeuvre but they weigh more. Backpacks are lightweight but difficult to carry when packed full.
My (hopefully carry-on) travel bags for lots of gear include a Lowepro Computrekker backpack or a Think Tank Commuter backpack, a small suitcase-style Lowepro Omni bag (not made anymore), a no-name laptop backpack and a Pelican 1510 roller case. I also bring an empty waist-pack in my checked luggage.
I worked with another photographer a few months ago who flew into Toronto with 12 checked cases of photo and video gear.
When checking studio strobes, I've always removed the flash tubes and modelling lights and wrapped them in lots of clothing in my clothes suitcase. I've packed some lenses and other photo gear, but never camera bodies, in my checked suitcase of clothing.
If you're worried about lightstands, softboxes, umbrellas, etc., being broken in transit, consider a wheeled travel case for golf clubs. It will have to be checked but some of these cases are quite strong. Most golf travel cases are big enough to hold a lot of your clothes, too. Your clothes can prevent the lightstands from rattling around.
You could wear your photovest and stuff the pockets.
In any case, expect extra luggage fee$$$$. When an airline quotes an extra luggage fee or overweight fee, it's just for one way. For connecting flights, separate luggage fees have to be paid to every airline involved.
Be sure your stuff is insured. If applicable, make sure you're covered for travel outside of North America.
Like David mentioned, if possible I'll drive rather than fly. I've driven 9-hours one way just so I could have all my gear with me. Also once did a two-day drive with lots of lighting gear: driving + cheap motel = easier and less stress than flying.
You'd think Uber would come out with a "flight sharing" app.
As for being a pack mule: two photographer friends of mine now use an assistant 100% of the time. No exceptions. Simply because it's now too much stuff for one person to carry. Hey, every pro golfer uses a caddy so why not photographers?