Just the first episode to start
Four episodes down, one to go. That's if, like Darren, you're playing Minecraft: Story Mode on something other than Wii U. For that port, you'll have to wait a few more days.
The first episode, The Order of the Stone, releases on the Wii U eShop in North America and Europe on January 21, 2016. It'll be $4.99, with the option to buy the full season pass for $19.99. Telltale says it expects later episodes to grace the Nintendo console "in the coming weeks."
As for system-specific features, you're looking at "off-TV play and mirroring, so players can continue the story on the Wii U GamePad controller, as well as seamlessly integrated touch-control options that allow players to use the joysticks and buttons or simply tap and guide the story directly on the screen at any time."
I can't say this one is high up on my list of "episodic adventures to just hurry up and play already." Not while The Walking Dead: Season Two and King's Quest are sitting patiently on my PS4.