Hello and welcome!
I agree with finding a "routine" that works for you. Everyone is different. I also agree with getting a good brain sheet! If you search brain sheets here on AN you will find a lot of examples...you can use those or take a look at them for inspiration and make your own sheet. What is your nurse-to-patient ratio on your floor? I work on a progressive care unit and ours is 1:4.
I get report and then go into the room with the off-going nurse. I say hi and introduce myself and this also gives me an opportunity to do a quick eyeball assessment of the patient. I then tell them I am going to finish getting report and I will be back to see them. This also helps me determine who needs to be seen first.
Depending on who is giving me report, I will go into the patient's chart and look up the most recent lab values, eyeballing everything but I especially pay attention to the patient's H&H, WBCs, electrolytes, BUN/Cr, BNP, PT/PTT/INR & troponins/cardiac enzymes and anything that may be really out of whack. I look up any test results (CXR, MRI, CT, etc). I look up allergies if they weren't given to me in report (usually they are except for the ones with the huge grocery list of allergies, I just tell the off-going nurse I will look them up in the computer). Then I quickly look at the meds I will be giving during my sheet. On my brain sheet I have all of the times listed in a row (19 20 21 22 23 00, etc...) and if I have meds due at a certain time, I will circle that time (so if I have meds due at 2100, I will circle 2100 on my sheet). This entire process of looking up information usually takes me about 10-15 minutes.
I think make my rounds, do my assessments, pull my meds and start my med pass. If patients have meds at 20, 21 and 22, and there are no contraindications, I give them all at around 2100. I cluster things as much as possible. You will eventually learn how to manage your time and develop a routine that works for you.
I also like to note that I always arrive to work EARLY - around 1830-1835. I find that arriving earlier instead of at 1845-1850 gives me extra time to get situation and look things up and gives me a head start on the shift.