How to add a Selection drop-down in a Grid

Can someone please advise me how to do this please.

I have a GRID app (not an editable grid view), and I need to add a Select field (with each record shown). Such that when the user clicks on the Select it shows various options which I would have added.
This ultimately would replace the numerous fields I have had to add as HTML fields with links or ajax events associated with each. Thus saving incredible space in the grid.

The only way I can think of is to add a new field, make that of type image, apply a suitable image and then apply a link to this image to a modal form.