Millumin uses mainly the graphic card, so the better your graphic card, the better performance.
You can compare graphic cards scores on this website.
For example : if you buy a MacBookPro, be sure to choose a model with a dedicated graphic card (GeForce or AMD, not only an Intel one).
As an example, a configuration with a MacBookPro Retina 2012 is able to run 4 x 1080p screens easily, even with big files.
See this test.
eGPU are also becoming a very serious alternative to get very high-end graphic cards.
More info on this post.
The drive is important too. If you got big files, you need a good one, that can read fast : for example an internal SSD, or a fast external hard-drive.
For codec recommendations, please read this post.
The CPU speed or the RAM size are not very important nowadays.
At last, if you uses multiple graphic cards, keep in mind that rendering can only be done by one graphic card, and the result must be pushed to other graphic card, which is time consuming (the other softwares have this limitation as well). More informations here.
Of course, we are working on better integration of multiple graphic cards, but we cannot promise anything for now.
By the way, be sure to click on the "Optimize" button, and follow the recommendations.