In face select mode, select faces by triangle/quad/other.
Available through header menu, toolbox, or hot keys.
Hot keys are:
ctrl-shift-alt-3: Select all triangles
ctrl-shift-alt-4: Select all quads
ctrl-shift-alt-5: Select all non-triangles/quads
(maybe a bit sore for the wrist)
And also available through the menu/toolbox.
I've never used f-gons so I don't know if the 'select other'
function works there (or works at all, for that matter).