First: Welcome! 
Considering the Era you want to play in, you might consider buying the Alpha Quadrant supplement. Beta Quadrant that is included in the Bundle of Holding, is probably of more value to your campaign, but you will find some iconic races of The Original Series and The Animated Series and information on Federation member worlds.
This seems an ideal campaign for a campaign on a Miranda Class Starship. In Star Trek II: The Wrath of Khan, the ship Khan captures, is a Miranda class. It has been in use during The Original Series and is still in use during The Next Generation (and even Deep Space Nine), so it’s a perfect fit on the timeframe you want to play in.
Plus, it’s crew compartment is only 26–35, ensuring the players won’t get “lost” in a 400+ crew ship and also allowing for the occasional staff officer to join away missions (not having enough red-shirts has its advantages 
).
I’m afraid that “the lost years” as some in this forums call the time period you want to set your campaign in, are hardly covered by the supplements we have seen until today. But you’re free to submit a request to the Official Product Wishlist in this forum. Maybe (and if it’s within Modiphius’ Licence!) the producers will think about a supplement dealing with this era. I would like to see that, too.