It is difficult to find a small, economical desktop computer suitable for classrooms. Mini-tower PCs are available for a reasonable price but take up a lot of desk space, or have to be located on a shelf underneath or knockabout on the floor. Large desktop screens can be difficult to see the teacher around. One option is a low cost laptop computer (15 Inch screens seem to be the sweet spot at present). These can be secured with a locking cable (with a cable tidy wrapping it with the low voltage power cable and Ethernet, for neatness). When not needed the laptop can be closed, making it easy to see the teacher.
What might help is a laptop stand: not the complicated and fragile adjustable sort, but a sheet of molded plastic, or perforated steel, bent to create a platform at about 12 degrees. The stand would need to be 500 mm wide, by 350 mm deep for a 15 inch laptop. This would raise the screen of the laptop about 100 mm above the table, for better viewing. The stand would extend each side of the laptop, so that cables could be plugged in and then secured in place by a cable tie through the holes in the stand (this would not stop a determined thief but would deter those who like to fiddle with computer plugs). A keyboard and mouse could be permanently secured and placed under the stand when not needed.
The closest commercial product I could find is the Cooler Master NotePal U3 Notebook Cooling Stand. But this has three fans, powered by a USB plug, which are not really necessary.