The report below for the sample credit union indicates that Checking (CHK) and Installment Loans (ILN) are the most common cross-sells to a new member -- the top 4 service combinations accounting for 72% of the household base are some combination of these two products plus Share -- but MSRs have mostly been trying to cross-sell Checking and Credit Cards (CCD) to new members instead.
The report also shows that a package for members driven by transaction (Checking) and lending (Installment Loan, Credit Card) needs will fare the best. Notice that the top 8 combinations of services, accounting for 86% of the household base, are combinations based on the Checking-Loan-Card services.