I do both. It mostly depends on the shape of the appliqué. For irregular edges with lots of tight curves and angles I usually do raw edge. For straighter appliqués I prefer turned under edges. I especially like the Appliquick method: A stiff interfacing fused to the wrong side of appliqué with edges turned under around the interfacing, using a glue stick to keep them in place. The Appliquick tools are available online, but I think you could find inexpensive substitutes.
The appliqués can be stitched down by hand or machine for the turned under method.