Age of credit matters to your credit report. Interest rates matter to your bank account. If you have $100 a month to put toward paying down balances (over and above the required monthly payments, of course), focus on paying off high interest accounts. Then prioritize those by the age of the account. Pay off the newest ones first; that way you'll increase the average length of credit, which should help your score, but you'll also be able to more quickly avoid paying relatively high interest.
Of course, if keeping accounts open and having credit available could trigger additional spending and debt, it might be more beneficial to close the accounts. Only you know all the ins and outs of your financial situation, and like thumbprints, they're different for each person. Make sure you carefully evaluate your situation; only you know what can work best for your financial outlook.
There are many reasons to start on the path to credit repair. The biggest reason is that credit affects you every day. It affects the interest rates you pay on credit cards and loans, including mortgages, and can result in higher security deposits for rentals. It can also affect what you pay for insurance rates and what credit limits you qualify for. Good credit can also mean financial freedom where you don’t have to depend on cosigners to help you make purchases and secure loans.