I assume the existing tile floor will be removed first?

Yes

Choose the tiler based on his previous work and reviews. Let him decide the method as they all work fine if done properly. Last thing you want is to force someone to use a method they are not familiar with and then it not come out right as it will be blamed on you at that point.

The best installation method is one that is TCNA approved (They need the TCNA Manual to show you) and that is done properly, using that method. There are a lot of right ways. Just not as many right way installers. Even those who have "been doing it for 30 years" are usually doing it wrong. Having a TCNA Manual that looks like it's been opened a time or two is just one method of screening a tile subcontractor.

https://whytile.com/qualified-labor/ 

https://tcnatile.com/products/publications/2023-tcna-handbook-for-ceramic-glass-and-stone-tile-installation/

Each of those methods works when executed correctly. I've done all of them over time in various DIY renovation projects, and, to my knowledge, none of them have failed. I"ve also torn out failed efforts that used at least three of those methods, plus the ever-popular mastic adhesive on drywall approach. I'm about to re-do my son's bathrooms (mastic on drywall) and will use ditra, I think. Just seems easier and less prone to failure, albeit a bit more expensive for materials. (in fairness, the mastic on drywall worked fine for about 60 years)

The old fashioned oil based mastic was actually waterproof when it cured. It was a completely different material. Today's mastic is water emulsified, and water just reconstitutes it back into it's toothpaste state.

^^^ that makes so much sense as to the durablity of some of the older showers / tile surrounds that I have seen.