What should A post-closing trial balance should only contain?

A post-closing trial balance will contain, assets, liabilities and owners equity accounts.

Assets include, current and long term assets

liabilities include, accounts payable, notes payable or any other "liability" the company currently has.

Owners Equity accounts include such things as Retained Earnings and Capital

You generally have 3 versions of a Trial Balance, your Trial Balance, Adjusted Trial Balance, and Post-Closing Trial balance.

The post-closing trial balance is what you use once your expense accounts & revenue have been closed to the income statement.