First, if you're just using the drive for taking your image/video files to and from the computer lab, any drive with 128gb or more should do. Be aware that most manufacturers make different "levels" of hard drives (at least with spinning drives), that varied in price and reliability. An SSD will be less susceptible to damage when carried around. I believe, like most solid state devices, if they fail they tend to fail early in their lifespan. There is more to a hard drive than just capacity; read/write speeds will vary.
I think the teacher's recommendations were in the context of permanent storage and to make sure that students don't outgrow their purchase quickly. Also probably assumes storage of uncompressed images. Not much cost difference between 500gb and 1TB in spinning drives, but still significant cost difference (as %) in SSDs.
You can buy a bare drive (of either type) and an enclosure or you can buy one already within an enclosure. Probably best to buy one already within an enclosure. Either way, make sure it is usb 3.0 or higher (faster), not 2.0. Even if your computer is only 2.0, you'll want the faster interface for the future. Some also have a usb-c interface; might be useful in the future.
Here's
one example. You can toggle between 500gb and 1TB and see if the differential makes sense for you. Here's
another. Both represent what I would consider the upper end solution. You'd probably find
this to be perfectly adequate for your needs.