I’ve always been vocal about how I love the pre-made adventures released by Modiphius to a point that I have not seen an adventure that I expected to need heavy re-work before I could run it. Keep in mind though, that I only, on a few occasions, had the possibility to actually run them.
That being said: Both Signals, the adventure in the quick start rules (which is actually a part of the adventure released under the same name within the Living Campaign) and the A Star Beyond the Stars mini-campaign contained in the Starter Set worked well for me and my group(s). Both are designed to slowly go through the basics of the rules to ease the start.
If you don’t want to use these, The Gravity of the Crime, being centered on the Prime Directive, seems like a very good starting point. Yet, it’s a detective adventure and I, personally, always found those hard to run. This may be GM and/or group-related but I, personally would wait until I had a firm grasp at the rules so I could fully concentrate on the adventure at hands. Please note that it has been debated whether a trigger warning was appropriate for this mission (contains spoilers).
It has been discussed that Call Back Yesterday is a very intense adventure and good for showing (and maybe developing) characters, (spoiler) as it traps the player characters in memories of their past, advising the GM to draw those memories from the lifepath events during character creation. This might be a great start to introduce characters. I’m thinking about runnig this adventure very early (or even as pilot) in my upcoming campaign. But, depending on your players, this might be better for later adventures, as it is not easy to present a character one has just started playing.
And for my third recommendation: Have a look at Stolen Liberty which also focuses on the Prime Directive and reads like it blends in very well into TNG’s thoughtful approach on trying to “do the morally right thing”. It might require introducing Supporting Characters, though, which is probably a bit too much for a first adventure.
Caveat: Apart from the adventure Signals and the A Star Beyond the Stars mini-campaign, I have not yet actually ran these adventures, so your mileage may vary. 