I really need to watch some Star Trek...
I don't want to offend Star Trek fans here. I know it may sound strange, as being a 80s-90s person I didn't watch ST, maybe just few episodes, never really pulled me in.
I was more X-Files fan.
What do you guys suggest to watch first?
I know it was like Star Trek, then some New Generation etc
Which one should I Watch before I get to new Picard series?
Picard is a hybrid.
They can't use almost anything story-wise from The Next Generation (TNG) due to ownership rights so the story/timeline is ripped from the re-imagined JJ ABrams movies but with TNG Characters. Anything they use from older stuff is pretty well explained so you don't need to know Trek history to enjoy it.
If you do want to watch older trek...
TNG starts off rocky, season 1 was made using older scripts originally intended for the original series, as a result there are times the story is very out of touch with the times since the writing was 20-30 years old. By season 2 they started finding their footing and it got better. While I always thought it was the best Trek series, a friend pushed me to watch Voyager, which I dismissed for various reasons, mostly I think I was burned out on Trek as TNG has just ended and we had Deep Space 9 (DS9) running (which I tired of), so it had been years of not just one Trek series, but two.
Voyager is better, though it pains me to say so because I just preferred the characters I think. It relies a bit too much on time travel too often to get out of a jam, one of my earlier complaints, but it really was better overall I think and they do come to use it less as a plot point as it goes on. That said, the best Trek series, which I think suffered from being the last in a long line up years of Trek series is Enterprise with Scott Bakula. Like me, I think people just got tired of the series so it ended early, but it really was fantastic. Had there been a few years break between series I think it would have done much better, it was just too much Trek at the time.
The original series (TOS) was hokey, if you like Doctor Who style sci-fi it may be better, the movies based on it are better in my opinion. Despite being hokey, the original did venture into serious issues now and then. DS9, some say it got better much later into the series after they realized there's only so many stores you can tell stuck on a space station. By then I had already checked out. It had some interesting elements though.
If you want gritty, the newer movies and the Discovery Series. The movies are a bit too Michael Bay-ish for me, Discovery is sort of the anti-Trek, sort of like how Rogue One is for Star Wars, some people really hate it, others like it.