Conventional wisdom suggests you want 2-4 months "cash" for expenses in event of emergency (loss of job, other emergency).

This is good advice... my advice suggests that the "cash" portion of this can be better utilized within a budget.

Goal #1 is create a budget
Goal #1a is save 10% as part of that budget.
Goal #2 is remove debt. There is no "good debt". There is bad debt, worse debt and "I can't believe I financed that" debt.
Goal

everything else depends on the budget.