The right amount of cash is the amount that that helps you sleep at night. It's entirely subjective.
My family (wife, me, and soon to be baby) are supported entirely by my consulting business. We keep at a bare minimum six months of budgeted expenses in a "reserve" sinking fund which can be tapped for unexpected, uncategorized expenses but is primarily for use in a loss-of-income situation. We recently pulled a bit from it to pay for an attorney to draft our estate plan which will be paid back this month, for example.
We also keep about a dozen other sinking funds of differing sizes and projected uses and durations for planned non-monthly expenses. For example, we have our medical insurance max out of pocket set aside, as well as small funds for car maintenance and furniture replacement. We also have a dedicated travel fund.
The total amount of the funds plus next month's expenses (YNAB rule 4) is split between our checking account (10%), a high yield money market account (80%), and a Vanguard account holding VASIX (10%).
We have a new source of liquidity coming online shortly (a HELOC, just have to make an appointment to close) so we will probably be reallocating out of the high yield savings and into less liquid taxable investments soon.