Installed Ubuntu system
I refer to the answer by C.S.Cameron as a good candidate for this task. (This assumes that we are talking about 'IBM compatible PCs' with Intel or AMD processors and 64-bit architecture. As described by Melebius, you need other software for computers with ARM processors.)
Portability may be an issue and it depends on the computers, where the Ubuntu system is to be used. If a computer needs a proprietary driver (which is not FOSS and cannot be included in a free Linux distro), it should be installed into the system when running in that computer, so you cannot expect a 'one size fits all solution'.
But an installed system (that can boot in both UEFI and BIOS mode) in a fast USB 3 drive is portable between many computers and should be fairly easy to tweak with some proprietary driver for graphics and/or wifi when necessary.
Ubuntu OEM system
You may want to create a master system from the compressed image file and add some program packages, and then create an image to distribute.
A more advanced method would be to create an Ubuntu OEM system and make it boot both in UEFI mode and BIOS mode (and include the program packages that you want), and then create an image to distribute. This way there will be a wizard method to get different computer IDs (for the network) and user IDs in each final installed system.
In this case you (or one of your students) must do the work to make the system on the USB drive independent. The following links and links from them may help.
How do I install Ubuntu to a USB key? (without using Startup Disk Creator)
Persistent live Ubuntu system
If you need not add/modify the system too much, it might also work with a persistent live system, for example created with mkusb, and this solution might be easier to implement.