Can I seek to discharge some debts and retain others?

No. As a matter of full disclosure, you must list all debts owed and all assets owned. You may not prefer one creditor over another within the same class, e.g., you may not seek to discharge one credit card and keep another, unless of course there is no balance owed on any particular card.

Secured debts are treated differently.  In a chapter 7, a debtor may "reaffirm" the original loan terms of a secured debt and retain the collateral.  For example, a debtor may keep her car and continue the monthly payments during and after the bankruptcy, while discharging all of her credit card debt.  In a chapter 13, a debtor may keep property and continue paying on the loan even if she is behind on payments, so long as her chapter 13 plan provides for full repayment of the past due amount, or "arrears".