Hi Michelle,
I have exactly the same setup that you describe and it works very well. One licence covers all your computers. You need to buy an Android version as well.
I also use the Cloud sync which works very well. If you don't plan to edit on your phone then you might get by with just Wi-Fi sync but I've never tried that.
Updates are automatic. You will get a popup on your computer and the installation is quick (a couple of minutes) and easy. Likewise, the phone updates automatically.
You will here talk about people saying an update is needed for the Android version but I find it works well - I don't spend a lot of time editing on it though but I love the reminders that popup automatically and being able to access all my todos wherever I am.
The only thing about syncing (even with the cloud) is that if you move from device to device a lot then you will need to remember to manually sync (click a button - not hard but you need to remember). Similarly on the phone: the 'cloud' button is always visible and you click to sync. I don't know if other products manage this better with automatic / immediate syncing on changes being made but, if they do, then this comes with its own problems.
I've tried many other managers: Outlook, toodledo, rememberthemilk and others but this is by far the best.
Good luck