Do we know if we'll be able to go into this blind? I really like Star Trek Discovery, so I'm interested in this. I've saw enough back in the day to know the basics about Next Generation... Data is a robot, Jeri Ryan was a Borg, Riker was Picard's #2, but that's about it.
Even official accounts have been urging people to catch up on some TNG before watching Picard so I'd say they're hoping people
won't go in blind.
There was even an article about it on the official site:
https://www.startrek.com/news/your-ultimate-star-trek-picard-watch-guide
But that's a lot on short notice at this point, so
bare minimum I'd suggest the TNG movies
First Contact and
Nemesis. First Contact is pretty good. Nemesis maybe not so much, but some crucial moments seem relevant to the plot and it's also the last time we saw these characters, so it will show you where we left off. I think these two movies would at least give you enough of a foundation to get where we're coming from, and get your feet closer to solid ground.
I suggest these specifically because they directly cover topics and character histories that you will see referenced in the new show. The TNG era as a whole has a lot more to offer, but I'm trying to stay directly relevant to your goal (rather than just a 'greatest hits').
You can rent each movie for $3/ea on google/vudu/amazon. Six bucks and you'll have your starter pack for ST:P.
(But if youve got time by all means do more from that official list. The more you see the more will make sense. Particularly I Borg, Datalore, and The Best of Both Worlds p1&2 which are all chronologically earlier than the above movies)