I'm new as well (7 months in). Some of my colleagues would come in pretty early to look everything over in the computer. I stopped doing that quickly (often the assignment wasn't ready anyway). Also, some take report without looking at the computer. We do bedside report where both RNs go into the room and introduce the oncoming shift, and you should be looking at any relevant assessment items, IV drip rates, vent settings, drains, monitors, etc.
What works for me is that while I'm getting report (we use an SBAR sheet), I look through all the orders, vitals, and labs. I try to be systematic about it, so, for example, when we get to discussing vitals, I open the VS flowsheet and look at how the most recent set, as well as how they trend. I'll also make sure all labs were taken (and if they weren't you should ask why), as well as look at the MAR to ensure all meds were given (again, ask why if something wasn't). After that we go see the patients, I make sure there are no immediate concerns/needs, then I go back to the computer, look over the orders again, do my 12 hour check, write down the times for meds/treatments/etc, then I can go and start my assessments, etc.
Later in my shift I'll try to look at the most recent note from the team (and any other relevant note) so I can get a more complete understanding of what's going on, as well as more of the plan.
In my opinion, the best way is to combine the two styles you see. Yes, you should be seeing why something wasn't done at the beginning of the shift, but you shouldn't have to come in very early to do that. You can see that during report on the computer (and think about it, getting report involves obtaining the information you need to safely take over caring for the patient. That involves knowing vital signs trending and relevant laboratory data). Yes, the clinical presentation of the patient is what you treat, and is important, however you also need to know the actual values of the abnormal vital signs or labs.
Hope that helps