Sometimes rough edges around a cut-out will show up against a black background, but at other times, you won't notice them until you paste it onto your chosen background. In the case of your hanging pic, the edges would be much less noticable on a light background.
The size of the background dictates the size of the final result.
I usually check the size of my source figure in Paint first, and then check the size of the background in another Paint window.
If my source figure is large (high resolution) I can enlarge the background in Paint, to a size which accomodates the figure.
Then I import the images to Photoshop, which allows me to work in hi-res without having to drastically reduce the size of the figure (which would otherwise lose resolution.)
The final result can always be reduced if you want a lower file size for posting.
I usually submit full size, hi-res manips on DeviantArt, and either host them there for showing here, or create an alternative 50% reduction version to post on this site.
Please ask if anything doesn't make sense.