I already have a mount where the monitor will screw into.
On the monitors I was looking at last night, there was a bracket on it. Several different types. One for mounting on a monitor shelf (like you mentioned) and the one I'm looking for mounted here:

See the chipboard? It screws into the edges.
I'm going to need a (unsure of the name of the thing, but it's sort of like an open cage)
I'll see if I can find a picture of some monitors to clear things up a bit more.