Oh I envy the group setup you describe!!
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I use a classroom with flat tables where students bring their laptops. All students have laptops in the class (and if they didn't I'd be working with the department/university to get them loaners). Laptops in class are used for team work a huge majority of the time (as opposed to individual work) so really they just need 1 laptop per team.
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I use RStudio Server. We discuss the reasons for this at https://peerj.com/preprints/3181/, but in a nutshell the goal is to get students started quickly without installation hassle initially, and then teach them how to do a local install later in the semester when they're all a bit more comfortable with R, and errors.