I agree that getting the most useful information at report and prioritizing based on that will be key. I come in for third shift, so it's slightly different because some of my patients are (theoretically) sleeping. If you have a complete handoff report, you shouldn't need to do much research, if any, before seeing your patients. I am personally not as concerned with what a note/lab/computer charting says, as I am with putting my eyes, ears and stethoscope on the patient. I would estimate that report is usually done between 11:30 and 11:40pm. By 12:30am, I've usually seen everyone, in order of most critical to least, and I've done my safety check- name and date of birth compared with bracelet, checked what's hooked up to the patient- IV, O2, Foley, etc., and asked if they are having any pain. It doesn't always work out that way because if patient's number 2, 3 and 4 all need pain meds, now we're past 1am before I've seen the others.
Use your available resources. If you're lucky enough to take report on all your patients from one nurse, ask them- based on this assignment, how would your prioritize my next steps? Everyone was a student at one point, and everyone was a new nurse. There's no problem with asking a question to help you learn the best approach and any nurse should be willing to spend a minute to go over the assignment quickly for prioritizing. After you've seen everyone, then you read the notes, labs, etc. If you see a sodium level of 126, you might be very concerned, but if you've been in and spoken with your patient and there no complaints of weakness, fatigue, headache, muscle cramps, etc- that's might not be out of the person's baseline. Also, many people will share with you important information like "my sodium always runs low because I drink a lot of water", during an initial conversation.
It will all come with time, don't worry too much, you sound like you're very much on the right track. And meds will come with time, you'll start seeing some of them over and over and will not need as much work there. Good luck!