I’ve not read all of the responses, but from what I have read, they’re full of excellent advice.
For myself, I suggest making a comprehensive list of the desktop software that you’re already running and see if there are Linux versions available, or close enough alternatives. For example, I use 1Password as my password manager and there’s a full-featured version available for Linux. By doing this, you’re in an even better position when your boss eventually raises this point.
Then, picking up where @JustNick left off, take a look at the software that your clients/customers use and see if there is anything that might cause an issue. Something might. But, there might be a workaround as well. So don’t right anything off before you’ve checked.
In short, anticipate the questions that your boss will likely ask as much as you can, and frame the transition through the perspective of the value and benefits that it will bring, rather than the associated cost or individual features. That way, you will come across as genuine and prepared, someone that your boss should listen to, and your boss should see this as a win.
Then, I suggest setting up a machine with Linux and using it on a daily basis for about a month or so, tuning/configuring it through the course of that time so that you get hands-on experience with what it’s like using Linux instead of Windows. Plus, you get to refine your approach during this time as well. Then, if the boss accepts your idea, you have something to base future company/organisation-wide installations off of.
I don’t have a specific distribution or desktop that I recommend, as so many are so very capable, and I don’t know your exact situation. That said, I use a reasonably customised Gnome Shell desktop on Ubuntu Linux and find it to be extremely efficient and performant.
I hope this helps in some way.