Your options are cardboard box, soft shell case or hard shell case. They all have their pluses and minuses.
I had a trip planned pre-pandemic and decided on the
Post Carry Transfer Case. The reason I chose this case was based on reviews. This case and the Pika received the greatest testimonials on other bike boards. Another reason I chose this case was I had to think about my destination and transfer within that country. My trip was to Japan and I would have had to take the Shinkansen and they have very strict rules about bicycles and luggage size for transport. For this reason I chose a case that brought the bike to it's smallest dimensions. I am well versed in bicycle assembly and disassembly, so that is not an issue but it is something you need to think about.
This trip I was going to bring my Trek Domane because I was going to ride long distances but if I were just riding in a city, I would go another route. I own a Brompton and a hard shell travel case. This is very close to airline legal, so you can get away with it and it offers the greatest protection. There is no assembly needed at your destination. Just unfold and ride. This was one of my easiest trips with a bicycle.
I have also done the cardboard box route and it worked fine getting there. I assembled the bike at the airport and rode away. Coming back it was difficult to find a box because I came back in a hurry. There is minimal disassembly and as mentioned every bike in the world comes in a box from the manufacturer.
Another trip was to Paris and I used a minimal bike bag. It worked but it was nerve racking. I was able to just carry my bike onto a train then subway from the airport and to my hotel. Paris subways are small and full of tourists with luggage so you have to plan around this. It worked but I would never do it again.
Last I did use a giant clear plastic bag once. Disassembled the bike to bike box dimensions and taped it together. This was good because baggage handlers saw it was a bike and didn't throw it around. It came back unscathed.
If I was traveling in the United States, I would use Bike Flights. For the record I have shipped a bike with them and it was easy. Pack the bike in a box, print a shipping label, drop it off at a UPS store. Pick it up at your destination or have it sent to the hotel. This way you don't have to deal with bikes at the airport.
Have a safe trip.