I've used my RP 2 and 3 for Raspicast (to cast from my Android phone), and OSMC/Kodi (for streaming). I've been away from it for a while, and would like to know if/how I can do both with my 3b. Do I dual boot, and if so what operating system, or is there one OS that will handle both my needs?
Asking for the "best" OS is usually with little meaning only. In this particular case - to provide Kodi and a target for Raspicast - any reasonably current OS for the Pi should do, if it has kodi, OMXplayer and OpenMax Image Viewer available. The recommendation would usually be to pick one of the more common ones, e.g. Raspbian. Benefit of that decision is to have the OS and the process of installation well documented (tutorials and how-tos, e.g. here and here) and have a vivid community to ask specific questions if one encounters problems.
This task should not require a dual boot system... with one downside, Raspicast does not work with Kodi being up and running. So using Raspicast would require to exit Kodi and start it again later.
According to this there is one alternative that makes use of Kodi itself, see section "You Can Also Cast With Kodi!":
[...] the Kore remote control app for Android devices. Usually, you’ll use this to remote control Kodi, but it’s also capable of casting to a Kodi system, including OSMC. Simply install the app, set it up with the IP address of your Raspberry Pi, and then head to YouTube. As with Raspicast, tap the Share button on the video you want to cast, then select Play on Kodi.