I know how to put different Linuxes on a live persistent usb, but I have noticed that updating/upgrading a such system increases the risk of breaking it.
From my experience it looks like the persistence feature is just an enhancement that provides some space for supplementary changes like installing an office suite, some multimedia players, internet browsers, and for the settings made inside applications. But persistence space is not meant for changes in the system files or in the important drivers. Attempting such changes seems useless (they are not remembered) or dangerous (the drive would not boot after a while). I have asked a specific question on this - here.
I know I can disable updates but what type of distro would need them the least - that is - would be meant to update rarely and not need a lot of update-upgrade considering the purpose of being used on an usb flash drive?