Should I play the previous Wolfenstein games before Wolfenstein II?

Wolfenstein II: The New Colossus came out recently. I know that it is a sequel to Wolfenstein: The New Order, which is itself a sequel to Wolfenstein (2009), etc. etc.

How much does the storyline depend on the storylines of previous games? Will I be missing out by starting with Wolfenstein II?

Without giving too much away, Wolfenstein II continues exactly from where Wolfenstein: The New Order finishes.

The characters are the same, and not playing the first game means you miss out on building the relationship you otherwise would. Would also be missing out on key information on why exactly certain things are happening or why they are the way they are.

You would be missing out on a lot of storyline information by starting Wolfenstein II before Wolfenstein: The New Order.

Another thing, Wolfenstein: The Old Blood is also worth playing, which is a prequel to The New Order.

I would say that you should definitely play the The New Order prior to the New Colossus. There is a point in the New Order story line where

General Deathshead makes you choose if you want to have Probst Wyatt or Fergus Reid executed. Depending on your choice, you can continue the story in The New Colossus as you had in the New Order (you get to make the execution choice again in The New Colossus).

So for consistency, you may want to play the New Order, make your choice, and then continue that choice in the second game.