What should I pay first to clean up my credit score?

Payment of derogatory items on your credit report will not improve your score. The damage is done and will continue in the remaining period of 7 years, whether paid, settled or not. However, lenders review your credit report whole, not just the score. Paying old debt looks better.
 
Get a copy of your credit report (AnnualCreditReport.com).  

Start with the most recent repeal and work back to the oldest. The age of an item, the less impact on your score. If it is near 7-year mark, you can let it out of the age.  

Depending on the age of default, must be able to negotiate a settlement of 25% to 50% in the payment of a lump sum payment. Forget about the payment plans. It is best to keep up until a lump-sum tender. Get any settlement agreement in writing beffore you pay and not to the collector of direct access to your bank account.
 
You need at least 24 months of constant

On-time payment history to improve your score. If you do not have an open line, active credit credit card even if you hve to get a secured card. Use the card, wait for the return and pay the balance in full each month. To build credit and avoid interest.