Irfanview can do all that, and it is free.
The options you can do when Capturing are:
1) Full desktop, all monitors
2) Desktop, current monitor
3) Foreground (the active) window
4) Foreground window, the Client area
5) Custom rectangle
6) Object selected with the mouse.
Along with those options you also have the ability to make it a timed snap, or with a hotkey that you chose. You can also choose if you want the cursor captured at the time, and where you want the captures to be placed. Also what of the 20 different image formats you want it saved as.
Plus you can have the images open immediately open within an IrfanView window to edit, or just open then later with the great IrfanView tool.