How much video RAM to run 'Final Cut Pro' on a Mac Pro (2013)
The minimum amount of VRAM Apple recommends for running Final Cut Pro X is 256 MB. As a Final Cut Pro user myself (albeit a very light user), I find that 1 GB is sufficient, though I rarely put the program "through its paces," and the work you will be doing will likely be on a larger scale. 1 GB also happens to be Apple's minimum recommendation for editing 4K video and 3D titles.

Ultimately, it depends on how intensive the work you're going to be doing is. Are you going to be doing intensive work with 4K content? Or are you going to do smaller home video-style projects? It may be useful to use Apple's recommendations as bases for comparison as you make your decision (see below).

To view the entire list of minimum system requirements, see Apple's Final Cut Pro X Tech Specs page. This Apple Support Communities discussion also has some interesting details about VRAM and how it applies to Final Cut Pro X.