You should always make the minimum payments on your credit cards, no matter what. Anytime you pay less than the minimum, you're considered late. Not only will you be charged a late fee, your interest rate might rise (if you're 60 days delinquent) making it more expensive to carry a balance.
After 30 days, your delinquency is reported to the credit bureaus and added to your credit report. A single late payment in your entire credit history might not do much damage, but the more delinquencies you have, the worse the affect your credit score will be.
You should get caught up on any accounts that are behind. Again, as long as you pay less than the minimum, you'll continue to be assessed late fees and have your late payments reported credit bureaus.
If you have any extra money in your budget after making your minimum payments, put it all towards bringing your accounts current. If you're late for 180 days or more your creditor might charge-off your account or refer it to collections or both.
Anytime your credit cards go beyond your credit limit, it raises red flags to current and future lenders. It causes them to wonder if you can responsibly handle credit. Plus, you face over-the-limit fees if your credit card charges this fee and you've opted-in to having over-the-limit transactions processed. Similar to getting current on your accounts, put your extra money toward bringing your accounts below their credit limit.