Overdue update...
Logitech MX Master - I do not have that mouse. The name was so familiar because I *almost* bought it. I really wanted it. The "horizontal scroll thumb roller" really attracted me. I thought it would be awesome for scrolling on timelines and stuff like that. But I tested it, and found that some of my applications didn't recognize it the way I thought it would. And in other cases, the normal up/down scroll wheel would scroll the timelines anyway. Is rechargeable with included micro-USB cord. So there was a lot I loved about it, but for the price I decided to pick something else.
Logitech Performance MX - That is what I got instead of the MX Master, and am using it on my primary desktop PC. When I first held it, I thought the "thumb indentation" was too tight and narrow, made for very skinny thumbs. But after giving it a second chance, I am quite happy with it. If I don't try to stuff my thumb into that area, it's fine, and in face, it makes it extra easy to lift the mouse because there is more of an overhang above the thumb. Is USB rechargeable; battery life is not nearly as long as the mouse it replaced, but is more than adequate, especially since it's easily rechargeable with the included micro-USB cord. Quite happy.
Logitech Triathlon M720 - This is what I am using on my new laptop. Its key feature is Blue-tooth connectivity, and the laptop has built-in Blue-tooth, so no adapters, not even a mini-receiver. Not rechargeable, but that's okay. The "triathlon" feature (switch between any of 3 paired devices) is of little-or-no value to me, but if you install the software, you could actually use the mouse to copy some files from one PC to another, which could be convenient in some cases.
MY MUST-HAVE FAVORITE FEATURES - First, it has to feel good in the hand. My main difficulty when shopping for the "Performance MX" was I was replacing a mouse I'd owned for several years, and liked (but the scroll wheel was getting jittery), and I could not find a new one of the exact same model. (People were selling used one for $100 or more! Yipes!) My other two must-have features are: 1) Both forward and back buttons, which is great for stuff like reading this forum. Read a post, and click "back" to return to the listing. Very convenient. 2) A "thumb button" is something I've grown accustomed to. It's "hidden" where your thumb rests, and the Logitech software lets you reprogram it. By default, it's the application switcher, that displays all active windows. But I reprogram it to be my MUTE button, so if I'm listening to music, and music player is minimized or buried, and I get called by a family member, a simple press of the thumb will mute the sound, no hunting or searching required. Oh, I also like the ability to switch between clicky-scroll and smooth-scroll. I don't switch every few minutes, but enough to appreciate the feature.