Accepted answer
Answering this needs to distinguish screening from monitoring. A screening panel looks for the unexpected; a monitoring panel tracks something you already have a reason to watch.
A sensible core for this population is a full blood count, renal function with electrolytes, liver enzymes with bilirubin, a fasting lipid panel with apolipoprotein B, HbA1c and thyroid-stimulating hormone.
Haemolysis in the sample raises potassium and several enzymes spuriously. If a result is bizarre, ask whether the sample was flagged before building a theory on it.
Pre-analytical factors — posture, tourniquet time, fasting, sample handling — are the largest source of error in routine biochemistry, well ahead of the analysis itself.
Nothing here is medical advice. If something is out of range and you do not know why, that is a consultation rather than a research project.
One out-of-range value on a twenty-analyte panel is expected. Two on a repeat is a finding.