If you want to keep all the video image then use 'Effects' tab >> 'Movement effects. >> 'Size/position and slightly reduce the area. You would then put a background in a higher track (lower number) to show behind. A friend often makes his background images using a single frame from his video and adding say a sand or blur effect so it's not to busy and distracting.
Alternately you could crop your video image by placing a border image in front of it (border on a lower / higher number track). The area in the center of the border image would be made transparent using Chroma key effect eg you can set white to be transparent.
An advantage of the second method is that the border need not be a perfect rectangle.
As soon as you're happy with a border / PIP combination, select both and group them so they will remain aligned if you decide to place them elsewhere.
If you decide to do several PIPs of the same size you can right click on the small clip and pick 'Copy video effects' and then on a new clip do another right click and 'Apply video effects' (exact wording may vary). And there is an option to save the effect to the user effects area and then load it onto any clip you like.
Another idea... Place a solid black or other color rectangle of the same size as your PIP clip behind (on a higher track). Offset your clip slightly up and to the side to give a sort of 'drop shadow' effect.