Now that’s a story that justifies it all 
All cool, and sounds interesting - I wish my current game openings were likely to last long enough to do that kind of ongoing game. I’ve got a 2 hour slot every week for the next 4 or 5 months, so I tend to think in terms of “mini-series” with a definitive storyline!
My group meets once a week for about 6 hours unless something comes up and people can’t make it. (Friday nights from 6 pm to Midnight.) The only problem is keeping everyone interested in playing Star Trek long enough to get to the point where they get their own ship, and then where to go from there.
One of the other guys that regularly GMs tends to get bored of other people’s games fairly quickly and wants to run something of his own fairly often. We also just had 4 people join our group in the last month and a half who are still feeling out the group and if they will remain for a while.
So, I have my work cut out for me not only with those issues, but also the fact that I don’t have much experience as a GM and prefer to be a player myself.
I find that many people want to play with a small or old ship to get started, which is something others alluded to in this thread. It makes sense: it’s smaller, the captain has fewer responsibilities, etc. Thus, a rule of thumb for this situation might be to get a scale 3 newer ship or scale 4 older ship.
However, I would counter that a Consellation class being refitted for the dominion war wouldn’t make too much sense, since very few functions on that class of ship were automated (and it would therefore stretch the federation’s already-thin resources all the more).
My suggestions echo some of the above:
Oberth
Sabre (From Command Division Sourcebook) - my personal recommendation given the story of being assigned as a starbase assistance vessel, though constellation also fits
Nova
Centaur
Miranda
Constellation
Just my 50cent:
Tell the players your intention and the style of the campaign you wish to create. And tell them, why you wish to limit the possible available ships. In my experience, if the players knew, why do you limited the choices, the campaign goes much smoother, and all have much more fun.
Perhaps you could even ask the players for preferred class and outfit, but they have to bring an explanation for their choice, and why this would be fitted in your intended campaign?!
The Constellation, with refits, would be no less automated than a Galaxy class during the Dominion War. The refits are what brings it up to the latest technology. It might not have neural gelpacks like the Intrepid, Luna, and a few possible others, but it won’t be as if it just came out of the shipyard when it was first commissioned 80+ years before. In fact the Miranda is older than the Constitution, and it was a workhorse that fought the Borg and the Dominion. Sure, most may have been relegated to supply convoy duty and border patrol away from the front lines, but they could still hold the line if needed.
I get where you’re coming from, SSiron, and I had the same thought too. The reason I made those suggestions was because the act of refitting such a ship (despite the previous major refits) would likely cost as many raw materials as a scale 3 vessel (in my opinion). Of course, the GM can choose what he wants, but I respectfully hold that the alternate argument (running a newer Scale 3 vessel) makes more sense.
Not really, because with the older ship, all you are doing is stripping out the outdated technology and replacing components. ‘Building’ a new ship from scratch is a lot more expensive resource wise, because you have to start from scratch and build the outer hull and all the rooms. 
As for running a newer scale 3 ship making more sense, that all depends on what time frame you are playing in and which scale 3 ships are available. My campaign is going to be starting in 2369, and at that time the only scale 3 ships available are the Oberth and Nova. 
It’s definitely an oddity of this system that refits can make 80-y/o designs almost entirely equivalent to brand-new cutting-edge vessels.
I don’t think of this as a feature; it’s bug to me.
Well, I also think that is one reason why they limit the number of refits per system to 2, and cap any increase at 12 for the Systems attributes. (Not that a lot of ships will be able to get to 12 in many Systems.) Also, you are only allowed 1 attribute increase every 10 years of service. So for the Constellation example, it won’t get another increase until 2375. It is technologically still a few years behind the top of the line ship in 2371.
I disagree with your view of it being a bug, I look at it as a logical use of resources. It is easier and cheaper on resources to upgrade an existing ship (and keeps the ship out there for longer) than it is to build an entirely new ship of the same scale and general purpose.
It’s like getting a tune-up or repairing a transmission in a car.
This is an area where abstraction and player enjoyment take priority over technical accuracy. No, a refitted Excelsior won’t be as good as a brand-new Galaxy. But if old ships are categorically worse, then that deters people from playing them. Equally, the differences between ships aren’t just in the attribute scores, but are in the sum of all the details of a ship. The game isn’t really built to care all that much about the marginal details that might distinguish different classes of ship (in part because the majority of that information literally does not exist - we know lots about the hero ships from each show, and next to nothing about everything else). It’s abstracted down to a level where, as long as the effect in play is close enough, we’re happy. An individual GM can use traits on a ship to highlight differences more, at their discretion.
And, well, something kept all those old Excelsiors in service well into the 2370s… and “the ease of reusing the old filming model” doesn’t work as an in-universe answer.
They also brought up refits a few times in the shows and movies. If I am not mistaken, the Enterprise from the Motion Picture was just coming out of drydock from a refit. Also the episode of Next Generation with the Bynars had to do with them performing a refit of the computer systems. It’s not just an easy way of explaining making older ships more enjoyable for players, in my opinion.
As a ship tech nut, I’m going to disagree with you there The earliest “official” date for a Miranda is in the mid 2270s, while the Connie goes back to 2242 (canon). Fan speculation aside, there’s no evidence there was ever a TOS-era Miranda, although 1 or 2 of the DIS classes may be equivalent.
A fairly major one. Officially, it also got a refit between the Pike and Kirk eras - hence the changes in nacelle design and crew complement between The Cage and the main series. Again by DIS, this was rather more substantial!
The Excelsior and Miranda both have big roomy hulls that could theoretically be stripped out completely and refilled. Lots of room for oddly-shaped new components!
Now that makes much more sense!
Correction withdrawn 
Ha… Yes… didn’t even notice that it was a type myself until I read @StephenBirks post… Opened up several browser windows and even the core book to point out the age difference, then scrolled down, and… Oops?
As a minor note re: the Miranda. It may not be and probably is not older than the Constitution, but it was likely in service during TOS, before the 2270s. A status board at Starbase 10 (I think?) displayed NCC-1864 as receiving orders or service or something. Point being that a ship with Reliant’s registry was active in Starfleet during the original series.
Not a very important point, but nerd eyes occasionally spot pointless bits which can be used in later gaming.
But that is the kind of thing I try to notice and I can’t believe I’ve never seen it mentioned in this kind of debate before! Memory Alpha confirms Starbase 11 in 2267… I’m sure Ex Astris Scientia mentions it somewhere but I’m going off that one.
It must be the same ship (same registration), so either the Miranda was already in service with the new look before the Enterprise refit or the Mirandas were refitted as well.
I am chastened. I stand corrected and tip my hat to you!
(Damn, after 20+ years, I need to rewrite my headcanon 
)
There are renderings on the web of what a TOS-era Miranda might look like.
I’d come across those, and they’re what I was referring to as “speculation”. I’m on record as saying I don’t think the refit was a fleetwide thing, and I’ve always thought the Miranda was a successor to something similar rather than a refit (I used Starfleet Museum’s Pytore Veliky).
Now, it appears I was wrong!
That particular image is nicely done, and it’s nice to see the Bombay being represented (ST Vanguard). Who’s the artist? The red lines seem to indicate it’s not Mr Metlesits. I’m assuming that’s a sensor pod up top rather than a navigation deflector (the Miranda’s is supposed to be hidden away in the hull - possibly the projections eitehr side of the bridge).