I would prefer a whole new crew, but with an existing class ship (prefereably a Sovereign, Constitution, Akira, NX refit or Excelsior).
As for setting, my preference is for TOS-movie era or just after (that gap between the movies and TNG). It's an era that doesn't get fleshed out much, but has a lot of potential. Klingons getting access to Romulan cloaks, the Romulan Empire going quiet, peace with the Klingons, Federation starship technology undergoing a renaissance (both in the case of the refit Enterprise and the Excelsior).
However I'm up for a 24th century series (just not post Voyager) and a Rise of the Federation like series.