I'd definitely go with Standalone. It shouldn't be much of a change in terms of usage — Zotero for Firefox and Zotero Standalone are nearly identical — but given that within days they'd be automatically upgraded to a connector in Firefox and need to download the separate program anyway, it'd save them the unnecessary hassle to just start with that, and they could also use their browser of choice to begin with.

@Roalderik one thing I would check before if you ask them to install Zotero during the course is : will they be able to install the standalone version on the computers in the classroom you will be using for the course (if you haven't asked them to bring their own device)

Up to now I was showing the Firefox version during courses because I know that my university, like a lot of institutions, prevents us from installing custom software, but have allowed installation of Firefox extensions.

I am now wondering how I will change my courses with the standalone version, I need to check with the IT department.

@asplundj thanks for the information. I had never tried as I am not often using a Windows' PC but tried it today and you are right, it works fine, I will now know it, thanks.