When entering the sale of a partially owned rental property, do I need to list the sale price (cash received) for my portion of the ownership or the entire house?

Yes, you will list only the sale price of the rental property for your portion of ownership in the rental.

Generally, income and expenses are allocated to each owner based on their percentage share of ownership.   For example, if two individuals owned a rental property, each owner would report 50% of the income and 50% of the losses or deductions on their individual tax returns.  This method is used when the property is sold each owner will report their share of the items related to the sale based on their percentage of ownership, which in the example above would be 50%.