I checked my ATAR first because I didn't feel great about a couple of my exams, so knowing my ATAR would give me an indication of how I did in a couple of couple subjects. I ended up with a higher SS and ATAR, but if for example I got a 35 SS for English ( a subject where I was aiming for a 45+ but the exam went disastrous) and a 97 ATAR, I would have liked to see the 97 first, estimate my English SS (since I know that it was key to my ATAR) and then prepare myself to look at the 35. Personally I would feel better about a 97 ATAR than a 35 SS in English. Some people also prefer to look at the ATAR first because it is so important for their course, such that it's basically the only thing it matters so that they get it over and done with.
I also see the value at looking at your study scores first, in the sense of preparing yourself before looking at your overall rank compared to the state.