Just a bit more personal info . . .
For nearly 6 years I have been using my 2012 Mac mini to edit FCP X.
It was the cheapest model with the i5 processor and 4GB RAM, though I did add another 6GB.
It have had no problems editing any amount of 1080p material. Obviously a more powerful computer would render and export faster but it is no slow-coach.
Over the past few days I have done a bit of testing to see how it handled native 4K and the answer is, no problem!
I added effects, green screen and transformational resizing to the clips and the unrendered footage played back without dropping any frames.
Obviously you will be getting something far more powerful but it shows what you can do with very little.