Need assistance with realistic photos.

I have been a fairly avid Photoshop user for probably 3 years. For that period of time, I have usually dealt with abstract art. Recently, I have started getting into realistic art, and using realistic pictures (ex: humans). I copy and paste these pictures into my current work, and of course, they are pixely, because the unneeded material on the outside was cut out with the Magic-Wand Tool. After it has been pasted, I do a Gaussian Blur on it. It looks alright, but I would like it to look a bit better. And by the way, Anti-Alias is checked when I'm cutting out the excess material in the background. Any help would be highly appreciated.

Try using the pen tool to select the object. Then make a selection from your path and use that.