Android: you can use an emulator on Windows and build on Windows to run on a local device. Android development is a slow and bumpy experience with device-specific issues and Xamarin.Forms has the most overhead on Android.
iOS Your app should perform well and not depend on device specifics. You will need a mac for development. I wouldn’t rely on LivePlayer esp with F#.
Also consider UWP for development, with momre occasional builds/releases on iOS/Android: Easy and fast development and debugging on Windows. Can’t release to Store. (Edit: this is possible now.)
7sharp9_exhumed convinced me on the slack channel Android Java is just not a good language to be developing on top of. So it looks like I’m opting for iOS.
Dave is right. If you are developing for Android then make sure you do have device with you. Running things on simulator or emulator is way too slow. While for iOS you will not find that kind of issue. And this very much generic for all cross platform tools.