It kind of plays out like a mish-mash of Bryan Fuller and Ronald D. Moore getting their way. While it respects the canon and history of Star Trek Voyager and Next Generation, it is not the style of either. It's grittier, it's not at all episodic, and it is thick with drama and has a slight non-linear approach (mostly flashbacks and dream sequences).
So far, the episode "The Measure of a Man" from TNG, Star Trek Nemesis, and Star Trek 2009 are probably good things to watch before Star Trek Picard, especially if you are hazy on them. Otherwise, having a general knowledge of Star Trek Voyager and Star Trek TNG are good too, as the series is a sequel to both. It might also help to watch the TOS film "The Undiscovered Country" which, while not linked by plot, is interesting for being a thematic antithesis of Star Trek Picard.
An interesting note is that the Romulans in Star Trek Picard feature both TOS style ridgeless heads and then there are those with head ridges similar to TNG through Enterprise; although the head ridges are less pronounced, and they vary from character to character. Romulans play an important role in the series, so I am guessing they wanted to give them far more variety.
New Romulan designs:
(NOTE: the one on the left in the below image is human, this is just the best pic I could find featuring two more Romulans.
There is A TON of exposition in these early episodes, so if you consider these spoilers, then skipped the rest of my post. Otherwise, I'll not go outside what we know from the trailer, but the background info might give enough to infer some of the events.
BACKGROUND SPOILERS BELOW
The plot reminds me A LOT of Xenosaga in the Star Trek Universe, which gives it all a very Ronald D. Moore feeling (which also had tons in common with Xenosaga). Like Xenosaga, decades earlier a scientist began developing synthetic human lifeforms - in Star Trek, it is scientist Bruce Maddox from the TNG episode "The Measure of a Man" cast as the Joachim Mizrahi - the scientist who developed the Realians. The Synthetics are the Realians. The Mars crisis where the Synthetics massacred the planet is identical to the Miltian crisis, even the cold eyes and blank expressions of the Synthetics match those of the Realians. This crisis is at the core of the conflicts going on with the franchise. Lastly, there is a female android who is a prophesied Destroyer, who, when activated, is able to kick all sorts of ass; two of them were made - although that's where the similarities end with the two (and we get into some spoiler territory if I explain the differences). Also like Xenosaga, there are a number of organizations involved, and even more secret organizations behind these organizations; one of them originated in TNG - the Tal Shiar, but others are new.
Lastly, I wanted to talk about the Romulan situation. Back to the Undiscovered Country.
In the Undiscovered Country, when Praxis (The Moon around the Klingon homeworld) exploded and destroyed the core of their civilization, the Federation successfully brought the Empire in. With the Supernova described in Star Trek 2009, the Federation under Picard began relocating the Romulans, but the Mars conflict occurred and the Federation commanded Picard's mission to end, as well, Spock didn't deliver the red matter on time, and as a result of Federation members threatening to leave if the Romulans were brought in: the Romulans were abandoned, and the Star Empire collapsed. This is why I called it the antithesis of the Undiscovered Country.
So far, the episode "The Measure of a Man" from TNG, Star Trek Nemesis, and Star Trek 2009 are probably good things to watch before Star Trek Picard, especially if you are hazy on them. Otherwise, having a general knowledge of Star Trek Voyager and Star Trek TNG are good too, as the series is a sequel to both. It might also help to watch the TOS film "The Undiscovered Country" which, while not linked by plot, is interesting for being a thematic antithesis of Star Trek Picard.
An interesting note is that the Romulans in Star Trek Picard feature both TOS style ridgeless heads and then there are those with head ridges similar to TNG through Enterprise; although the head ridges are less pronounced, and they vary from character to character. Romulans play an important role in the series, so I am guessing they wanted to give them far more variety.
New Romulan designs:
(NOTE: the one on the left in the below image is human, this is just the best pic I could find featuring two more Romulans.
There is A TON of exposition in these early episodes, so if you consider these spoilers, then skipped the rest of my post. Otherwise, I'll not go outside what we know from the trailer, but the background info might give enough to infer some of the events.
BACKGROUND SPOILERS BELOW
The plot reminds me A LOT of Xenosaga in the Star Trek Universe, which gives it all a very Ronald D. Moore feeling (which also had tons in common with Xenosaga). Like Xenosaga, decades earlier a scientist began developing synthetic human lifeforms - in Star Trek, it is scientist Bruce Maddox from the TNG episode "The Measure of a Man" cast as the Joachim Mizrahi - the scientist who developed the Realians. The Synthetics are the Realians. The Mars crisis where the Synthetics massacred the planet is identical to the Miltian crisis, even the cold eyes and blank expressions of the Synthetics match those of the Realians. This crisis is at the core of the conflicts going on with the franchise. Lastly, there is a female android who is a prophesied Destroyer, who, when activated, is able to kick all sorts of ass; two of them were made - although that's where the similarities end with the two (and we get into some spoiler territory if I explain the differences). Also like Xenosaga, there are a number of organizations involved, and even more secret organizations behind these organizations; one of them originated in TNG - the Tal Shiar, but others are new.
Lastly, I wanted to talk about the Romulan situation. Back to the Undiscovered Country.
In the Undiscovered Country, when Praxis (The Moon around the Klingon homeworld) exploded and destroyed the core of their civilization, the Federation successfully brought the Empire in. With the Supernova described in Star Trek 2009, the Federation under Picard began relocating the Romulans, but the Mars conflict occurred and the Federation commanded Picard's mission to end, as well, Spock didn't deliver the red matter on time, and as a result of Federation members threatening to leave if the Romulans were brought in: the Romulans were abandoned, and the Star Empire collapsed. This is why I called it the antithesis of the Undiscovered Country.