Don't know much about the Jamis. I would stay away from the Raleigh. And the Specialized will probably offer a really great ride quality, depending on model and condition.

My regular ride is a Specialized that I call my Junker II. The bicycle, though banged up and fitted with less than perfect components, is a joy to ride. In fact, I can't believe how nice the ride quality is for such a junked up bike...