We present an HDG formulation for a model Possion's equation on a polygonal/polyhedral mesh. We then discuss two approaches to devise HDG methods with optimal convergence (or superconvergence) property. The first approach is to suitably choose the stabilization function (or the penalty term) to get optimality. (This idea was originally presented in Christoph Lehrenfeld's Diploma Thesis [2010] under the direction of Joachim Schoberl) The second approach is to systematically modify (or augment) the approximation spaces in a suitable way such that the projection based error analysis [Mathematics of Computation 79 (271), 1351 1367] can be applied. (It is the continuation of the work started [Mathematics of Computation 79 (271), 1351-1367] on searching for "superconvergent" HDG methods) Preliminary numerical results on polygonal meshes are presented.