Hi all, just joined the site, so still getting up to speed (not exactly working on all thrusters, one might say!) I love discussions like this, though. I'm also imagining a post-Nemesis storyline, although a bit earlier than Samuel's - probably starting immediately after Nemesis and focused on an "every day" ship - a Nova Class assigned to DS9 for renewed Gamma Quadrant exploration, crewed by competent but regular people, not a ship full of prodigies a la every series and movie made!
Anyway, not to hijack the thread with my own idea! In response to Samuel's original post, I'm with those that say the Ambassador Class is probably the oldest in regular service by 2410 - maybe a handful of Excelsior Class ships still in operation under the command of veteran captains with strong personal attachments to the ships, unwilling to "trade up" to a new command and with enough influence at Starfleet Command to keep their grand old ladies in service. I would imagine them being phased out as said captains retired, however (similar to the Enterprise-A's presumed fate after The Undiscovered Country - soon replaced by the Enterprise-B after Kirk's retirement). I would like to imagine a big period of rebuilding, new designs, and a renewed focus on exploration and humanitarian missions in the years following the Dominion war, replacing many ships lost and retiring many that were damaged.