Single people are in class I, single parents in class II. Married couples and registered partners choose between IV/IV or III/V, or IV with a factor.
The tax class only affects the monthly withholding, not your final annual tax. That is settled in the tax return, which is why some combinations make filing mandatory.
Full guideTax classes in Germany, explained in EnglishRelated terms
General information on German tax law, not advice on your individual case.