I say fuzzy background. To do that, I would paint the background relatively "normal", and when the wet paint has set up a bit, I'd use a 1", clean, soft, dry, Taklon, flat brush, and beat the heck out of it, using random, criss-cross strokes, in a blending process. That will result in a very nice, appropriate "blur".
If doing that causes your paint to "spill over", or to encroach upon the main subject, just let it. Then, re-establish the main subject, either while the background is still wet (if you want to create a few soft edges), or after it has dried, if you're more interested in sharp edges.