The director says it's not necessary to see Blade Runner first
Director Denis Villeneuve said that he intended for it to be accessible to first time viewers.
"That was one of the challenges ... to create a movie that would be in total relationship to the first one, but could stand on its own," he said when we met to discuss the film in London recently. "I will say that people don't need to see the first movie to understand my movie."
—"Do I need to watch 'Blade Runner' before seeing the sequel?", CNET, October 4, 2017 (Emphasis mine)
But he thinks you should see it anyway because it's really good
"I would recommend [seeing] the first movie because I think it's a masterpiece," Villeneuve says. "One of the things I said to myself that could be a positive effect of doing [the sequel] is to to put back the spotlight on the original movie, for the generation that are too young to have seen it on a big screen or even at home.
—"Do I need to watch 'Blade Runner' before seeing the sequel?", CNET, October 4, 2017
Either the Theatrical Cut or Final Cut is sufficient
Villeneuve has said that the Theatrical Cut and Final Cut have different thematic elements and Blade Runner 2049 is "in between" (minor spoilers):
"The key to making [Blade Runner 2049] was to be in between," Vileneuve said. "[The theatrical version] is the story of a human falling in love with an artificial being, and the story of [the director's cut] is a replicant who doesn’t know he’s a replicant and slowly discovers his own identity. Those are two different stories."
—"Which Cut Is Blade Runner 2049 a Sequel To?", Den of Geek!, August 25, 2017
CNET's Richard Trenholm says you can watch either, since the major plot difference isn't critical to the sequel.
In terms of getting ready for the sequel, either would work. Fans deride the Theatrical Cut for its over-explaining voiceover and studio-imposed happy ending, but it still packs a punch if that's the only version you have access to. The Final Cut removes the voiceover and, more importantly, creates ambiguity around who is or isn't an android -- but that theme isn't critical to the sequel, so the choice is yours.
—"Do I need to watch 'Blade Runner' before seeing the sequel?", CNET, October 4, 2017
GQ's Scott Meslow recommends the Final Cut because the original director, Ridley Scott, personally oversaw it.
So there are like 27 versions of this movie, right? How many of them do I actually need to watch?
Just one! And Ridley Scott made it pretty easy to remember, because it’s the one called Blade Runner: The Final Cut. After years of confusion about the "real" version of Blade Runner, The Final Cut was released in 2007 to provide a single, definitive of Blade Runner. Scott personally oversaw a brand-new remaster of the original movie.
—"Everything You Need to Know About Blade Runner Before Blade Runner 2049", GQ, September 28, 2017
I haven't seen any recommendations to watch both before seeing Blade Runner 2049, unless you are personally interested in seeing the difference.
If you don't have time to watch the original, you can watch some short prequel films
There are three short films created as prequels to Blade Runner 2049 in order to promote the film and expand on the world. If you just want to get a sense of what the world is like, this is a good jumping on point.