Definitely the overdue bills if they are utilities/essentials. If they're overdue credit cards, you'll pay more in fees but they may have to wait until you get your electric bill caught up.
I think you would really benefit from reading a little bit of Dave Ramsey's advice. I started with DR about three years ago when I had $30,000 in debt, and "graduated" to MMM after learning what I could from DR's method. He advocates paying for the "four walls" first- housing, food, transporation, and clothing. Keeping up with your rent/mortgage and utilities is your first priority; it's hard to show up presentable at work if you're being evicted or don't have water/electricity. Next is food. Buy cheap food that meets your nutritional requirements. Beans, rice, potatoes, etc are all cheap and filling. Transportation to get to work if your next priority, though commute as cheaply as possible. Clothing is also essential, but most people can get by on what they currently own for a few months or a year while you get yourself out of debt.
Once you're caught up on overdue bills, DR advocates saving $1,000 in a baby emergency fund (as you mentioned) so you don't have an unexpected expense and end up behind again. Next, pay off all your debt. Many here prefer to focus on highest-interest rates first, which is mathmatically advantageous, but depending on how tight your budget is compared to your monthly minimum payments, sometimes you'll need to knock out a few small debts so you have some more disposable income to put toward the other debts.
Once you're out of debt, go back and pad your emergency fund to cover 3-6 months worth of expenses and then invest. During all of the above, look for ways to increase your income, decrease your expenses, and increase your financial knowledge. Continue reading DR, MMM, etc to stay motivated and learn more ways of increasing income and decreasing expenses. At milestones, congratulate yourself on how far you've come and then keep going. It's a marathon, not a sprint. But if you keep going, you'll get where you want to be. :-)