It isn't clear to me which era your story would be taking place in. TOS? TMP? Post-TMP? Pre-TNG? TNG? DS9/VOY? Post-VOY?
It's easiest in most of these eras to suggestion a Constellation-class vessel, which would seem to be a new design in roughly the TMP era. If your story were set in TOS/TAS or TMP, you might want to look at a Miranda variant (one without the torpedo "roll bar").
It was never clear to me what era the Centaur-class vessels
came from, maybe post-TMP. Depending on the era of your story, one of these might be ideal.