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Sankor can be had for as little as $150 on ebay. If you're just starting out you don't need a mint one really. And any of the 2x adapters are all similar. Yes they are heavy and will strain the lens mount a little, but it really won't make a difference. The speedbooster makes for a great mount and the Nikon lenses are old style metal housing which is really strong. If anything you'll have a hard time focusing with the weight on the lens. But you have to dual focus anyway (one for the Nikon, other for the Sankor). Most projector lenses are a minimum of 40mm m4/3 (85mm full frame). You still might get a vignette on the corners. 50mm w/ speedbooster on the GH4 4K will come out to around 85mm FF equivalent so you'll be right there. If anything shoot with the new version 2.0 firmware for the GH4. Then you can use the new Photo 4K modes, and if you shoot 1:1 (2880x2880 square) then you can stretch and crop the image using the center of the lens. This will reduce the vignette quite a bit and maybe you can shoot wider. You can look up Luke Neumann on youtube and see his quick tutorial on how to use the version 2.0 4K photo modes.

Slashcam tested the D750 video features, they even compared it to the D810 and GH4 here: http://www.slashcam.de/artikel/Test/Nikon-D750---Nikons-beste-Fullframe-Video-DSLR-bisher---Das-wahre-Leben.html#Das_w As I see it has about the same image quality as the D810, just a tiny bit softer.

Congrats. You're in for a treat.

A rig is not 100% necessary with an anamorphic lens of that size, all you would need is a clamp such as the Red Stan anamorphic clamp. You really only need a rig when shooting with the larger anamorphic projector lenses. If you're looking for a budget anamorphic lens I would recommend a Sankor. I had one and loved it very much. They are also small in size and can just be attached with a clamp. Mine was sharp even with a wide open taking lens ( I also used Nikkor primes with it ) and it produces great blue flares if that's what you're looking for.

Tokina 11-16 2.8 is the obvious and probably most favoured option. I've seen a lot of nice stuff shot with the 11-16/BMPCC combo.

Looks impressive!