There must be some limitations in the device, because the set of categories: saturated mono, poly, is exhaustive. (Trans can be either mono or poly, but overwhelmingly, trans are poly. See the Wikipedia article,
Trans fat.)
Below are generalities you've maybe seen already.
Avoid trans fats. This is getting easier as more and more countries ban them.
Minimize polyunsaturated, except for omega-3's, which are very health promoting. Aim to maximize monounsaturated and saturated. Meat, cheese, sour cream are high in saturated fats.
Maximize omega-3 fats, minimize omega-6. There's a lot of information online about this.
Wikipedia articles on various food oils actually tabulate the content of by fat category. The article on canola oil happens to contain a comparative chart of all the major commercial oils. (Canola oil's a semisynthetic oil that's disgusting, despite being fairly low in polys. It also made a scum in the frying pan when I tried to cook with it.) From this table, I learn something: there are healthy versions of two bad oils, safflower and sunflower. The healthy versions are the high oleic ones. But I read ingredient labels when I shop, and I don't recall ever seeing the phrase, "high oleic".