There are no "cheap" 120Hz monitors.
At ukpcpartpicker the cheapest they have is 274 pounds.
https://uk.pcpartpicker.com/part/asus-monitor-vg248qe
Whereas the cheapest 60Hz is 60 pounds. It's pretty crappy, but my point is 60Hz are far cheaper so you're going to have to decide whether you really need 120Hz or not.
*Since you mention CRT it makes me wonder exactly why you want 120Hz. On the CRT monitors you got flickering which was bad at 60Hz and arguably disappeared at 120Hz. However, LCD monitors are not the same technology at all so you don't get that type of flickering.