This should be your first lens for the Panasonic GH4. The 12-35mm 2.8 lens becomes a 24-70mm 2.8 lens with the MFT mount. At a mere fraction of the weight of its DSLR equivalent, it packs a powerful punch in terms of versatility for both video and stills shooters. Comes with Panasonic’s version of Image stabilization.
If you will own a GH4, this is where you start lens wise. I cannot recommend it higher.