Shutter speed comes first
In landscape photography you can let the shutter drift; in wildlife photography it is the setting that decides whether you have a picture at all. A blurred eye cannot be rescued. As a rule of thumb, use at least 1/500 s for a resting animal that might twitch, 1/1000 s for walking mammals and wading birds, and 1/2000 s or faster for small birds in flight.
The old hand-holding guide of "one over the focal length" was written for still subjects. With wildlife, the subject's own movement usually demands more. Stabilisation helps with your shake, not with a wren's.