The big boys they want to make games for the launch lineup.

Probably Squenix, Capcom, Platinum, EA, Ubisoft, Activision.

It'd be nice if they also included Bethesda in that, but not expecting anything.

Nintendo needs to get all major 3rd party publishers on board, particularly the western ones because that's where the money is.
Nintendo shouldn't really be picky though, it's that pickiness that has done so much damage with the video games market for Nintendo consoles, if they want to stay alive in this industry then they need to get kits to everyone and they also need to make games that appeal to the western market that buys 3rd party.

As an aside point any architecture comparable to PS4 and XB1 would be simple for 3rd party developers to port their games to. Nintendo should be stumping up the cash for porting costs and marketing for any titles releasing in the Fall of next year.
The NX console should be the superior platform for 3rd party games and the handheld should allow the unique prospect of gamers being able to play everything on the move if they want, this would be a great selling point for Nintendo.

Any dev kits going out now would easily allow 3rd party studios to get their games on NX for a 2016 launch, if the kits were released this time next year, then that would show a 2017 release. Even Wii U's architecture was relatively simple and pretty similar to XBox 360 (3 Core PPC, AMD GPU, with DDR3 main memory and an eDRAM cache). A CPU relatively close or even better than what's in PS4 or XB1 is easy to obtain, hell AMD's Puma or Excavator cores are much better.
The GPU tech available through AMD now has a better feature set, along with using less power to do more or the same as PS4's Graphics Core.

Nintendo are also a part of the Khronos board, which could easily mean that they're developing a version of Vulkan for use in NX, basically every 3rd party studio will be familiar with that API now.

Porting a 3rd party game to similar platform to PS4 and XB1 is a cakewalk, NX will no doubt share X86 architecture, likely using AMD's latest technology, the only doubt in my mind is how powerful it will be due to Nintendo's love of small form factor tech, though it is perfectly feasible for the home console part to have more horsepower than PS4 in a smaller package than that platform, AMD's latest tech is more efficient than what's in PS4 and XB1.

Only members of The Dream Team 2: Electric Boogaloo.

Anyone who wants one

Rockstar should be their priority...if they get next GTA locked for NX I think most, if not all western publishers will follow suit, if for nothing else but for "They're releasing on NX, why aren't we releasing anything? Bob, you're fired."

Where did I say "Summer"? Please read again...

I hope that Nintendo is managing to give dev kits to all the major publishers. They need to get their base on board certainly in Japan, but probably more crucial is for them to secure the support of EA, Activision, Ubisoft, and all these other Western publishers that I hate.

Why would Square get one of the first ones then, though? If true, wouldn't that imply that they're simply going after whatever publishers they can get interested? And why would Square be interested now when they've largely ignored Nintendo home consoles since the mid-90's?

Naturally, EA. They'll be invited on stage to announce an unprecedented partnership.

I agree with this