Once you have the image cut out(using the pen tool, magnetic lasso tool, etc), you right click the image and click "make selection", a window will pop up, put the feather from 0.5-1, depending on how rough the image is, then click "ok". After that, just drag the selection(the part you cut out, it'll have an outline around it) into your sig.
To resize the render after putting it into your sig, make sure you are clicked on the render and go to: edit - free transform - then hold shift(so the image stays the same quality when you shrink it) and size the render down.
Hope this helps.
“Anna, my strong, terrifying Anna.” -Cas
"You lack the requisite spine and testicular fortitude to study under me" -Elodin