Any USB keyboard will be compatible.
You need to look at what video output(s) is available on the new computer and what inputs your monitor has. If your monitor and new computer both have a VGA port, it will be compatible. More common these days are digital ports like HDMI. These can generally be connected with an adapter or adapter cable. For a common example if the new computer has an HDMI port and your monitor has no HDMI port but does have a DVI port. (The one exception that's a little more complicated is HDMI (on PC) to Display Port on monitor.)
Here is a picture of common connector types.