I'm not seasoned (8 months in), but I was taught to do a thorough initial assessment, then do focused assessments r/t the particular surgery. It really depends on the type of surgery, anesthesia, etc. Your facility will have guidelines for vital sign monitoring. I'm on a general surg/ortho floor.
Check pulses, cap refill, dressings, pain, urine output, vitals, IV site.
Dressings, pain, output, vitals, IV site
Don't forget to look under a patient to check for bleeding--the dressing could have a bit of blood on it, but more could've pooled behind them. Whenever you're in just checking on a patient, you can tell a lot quickly--skin color, LOC, changes that could mean you need to do a more thorough assessment.
I've also found that I have to check to make sure that patient's home meds are restarted after surgery. Sometimes the docs aren't great about sending the med reconciliation form to pharmacy.