You probably won't have any problems. If you are moving to an old monitor you can make the settings as safe as possible, that is not to have refreshment rate higher than 60 Hz and resolution at 800X600. Changing the settings depends on what distro you have. Normally you can just right-click at your desktop and select resolution and refresh rate.
If things go really bad you can edit /etc/X11/xorg.conf or /etc/X11/XF86Config, depending on which version of X you are running.
You might need to tweek the settings a little, but probably you will have no problems.
Good luck!
E