You shouldn't login to Sync on a (public) computer that isn't yours as this downloads your personal data to this device and may not remove it, so other that use the device after you can access to this data. Sync always works both ways, so data on this computer will be uploaded to your Sync account.

I am the last one who uses the computer before it gets wiped each night, so I am not concerned with my data remaining on it.

How does sync decide which settings to send to the cloud and which it receives from the cloud to override the local settings at the moment that you login?

Is it possible to tell sync to only receive and not overwrite on the initial sync ?

I don't think that the selected search engine is part of settings that are synced, so syncing preferences won't help you here. I think that Sync checks what is on the Sync server and data on the computer that is newer than what is on the Sync server or isn't present will be uploaded. To prevent uploading data you would have to clear all data that is included in Sync from the current profile before connecting to Sync.

• https://support.mozilla.org/en-US/kb/how-do-i-choose-what-types-information-sync-firefox

Can't you run a portable Firefox version on that computer to avoid having to use Sync ? The portable version comes with its own profile folder and doesn't interfere with currently installed Firefox versions.

• https://portableapps.com/apps/internet/firefox_portable