there may be free tools compatible with Visio, but for me, best tool is IRFANView icon pinned to taskbar.
Alt+ PrtScan for window capture
click Iview icon
^V (paste)
draw rectangle
^Y (crop)
^s (save)
choose file name and path... done
with practise, and repetition, takes me 10 sec.
IRFANView 32/64 is full featured menu optioned (not fat GUI App) image editor, resizer, compressor, save as any format, read any format and can use Adobe filters, Edit > show toolbar to add text, arrows eraser, clone zones etc.
Lean and fast but for those who prefer hotkeys. 100x better than MSpaint and faster than PSP, alternatives are GIMP.
But for single purpose screen save, use other suggested Apps IF you can use timed screen shot, flip screen ALT+Tab and capture array??