Straight or zig zag depends on the look you want. If you like frayed edges -- sort of shabby chic -- use a straight stitch a bit back from the edge. If you want it smooth go with a zig zag.
As for a pattern, Google free coloring book pages. You are bound to find a frog you can turn into a pattern. Anohter great applique site is
http://www.fourtwinsisters.com/