Should I make payment on the card with small balance or large balance?
FICO gives more importance to the recency, severity, and frequency of your credit card delinquency. The more recent and severe the missed payment is, the bigger is the impact. In my opinion, you should pay the account with bigger balance first.
It is better you talk both the banks and have an alternative payment arrangement if possible. Explain to them that you have some financial crunch for which you're not able to make the required payments.
But, tell me one thing, why will you make only the minimum payments? Why not opt for a plan that will help you get rid of the debt entirely? Opting for debt settlement can help you clear the debt by paying less than what you owe to them.
I would rather suggest you to pay off the card with highest APR first. Do as craigh suggested to you. Contact your creditors and have an alternative payment plan.
Settling your debts might be another good option for you. Your debts can be settled at a lower amount than what you actually owe.
Debt settlement is a good option as tiarajoseph has suggested. Doing so, you can clear the debts on both the credit cards fast.
If you can't do it on your own, take help of a settlement company and get rid of your debts.
You will just have to make a single monthly payment to the company. The negotiation will be handled by them. And, you will also get complete professional guidance.