When paying off multiple debts there is a protocol that many support. Payoff your debts according to the snowball method.
The snowball method proposes that you make minimum payments on all debts except the smallest one. Payoff the smallest debt as quickly as possible. As smaller debts are paid off, that makes one less minimum payment you need to make, leaving you with more money to put against the next smallest debt.
So in your case, pay off the smaller debt completely, then follow up on the larger one by making regular payments at least equal to the sum of your two current minimum payments. You'll see immediate progress in tackling your debt and have one less minimum to worry about, which can serve as a little safety of it's own if you have a bad month.
As to saving the thousand dollars, that is pragmatic and prudent. It's not financially useful (you won't make any money in a savings account), but having cash on hand for emergencies and various other reasons is an important security for modern living.
As suggested in another answer, you can forgo saving this thousand and put it against debt now, because you will have a freed up credit card. Credit can certainly give you that same security. This is an alternative option, but not all emergencies will take a credit card. You typically can't make rent with your credit card, for example.
Good luck paying your debts and I hope you can soon enjoy the freedom of a debt free life.