I have completed a few safaris in ZIM, Namibia and SA, the world has changed in the last few years, and more for Covid recently. My first hunts travelling with firearms was simple, fill in a form, have checked at departure and receive at other end in special baggage. Those days are long gone, now you have paperwork from Canada and then EVERY country you land in and fly out off. Then the SAPs in SA paperwork. Invite letter, permits and more paperwork, plus the gun haters/misinformed at every counter. If you want a layover in England good luck, research that closely and be ready to pay the $500 fee.
Your first question you need to answer is are you taking guns or ammo? If no then any flight, country and layovers that work for your trip are OK. If you want to take your weapon/s then your are severely restricted or have a fat wallet. Every airline has firearm transport fees, some are more than a new gun.
My 21 day safari for 2020 was postponed due to Covid and is now booked for June-Aug 2021. After a ton of investigating the best for me was/is Van-TO, TO to Addis Ababa, then on to Joberg on Ethiopian air. That route and flights are the only ones where the costs to travel with my rifles do not exceed the cost to buy a new gun or rent one. I can check all baggage straight thru. Last trip I went thru US, huge mistake, cannot check baggage thru and all firearms must be opened and inspected upon entry and exit. Make sure you have hrs at each airport as its a PIA. I am stubborn and for me it provides more gratitude knowing I hunted, shot and reloaded every round that I used to hunt those amazing critters.
For a first time flyer with firearms I would suggest getting a well versed knowledgeable travel agent. One that knows every airline and country's current regs. Or be prepared to do a ton of internet work and plan yourself. Worse is this dam Covid BS as its changed the face of travel, who knows what airlines will not be around when this is over. Just recently new rules and flights with guns within SA has become a huge problem.
Good luck.
MJB