Think of yourself as a business with two accounts, "cash" and "net worth". Your goal is to make money.
"Cash" is what you need to meet your obligations. You need to pay your rent/mortgage, utilities, buy food, pay for transportation, service debt, etc. If you make $100 a month, and your obligations are $90, you're clearing $10.
"Net worth" are assets that you own, including cash, retirement savings, investments, or even tangible goods like real property or items you collect with value.
The "pay off debt" versus "save money" debate, in my opinion, is driven by two things, in this order:
- Affect on your cash flow. (Think liquid cash)
- Absolute return. (Think investments that are less liquid, like a CD, or mutual fund with capital gains)
If you start saving too soon, you'll have a hard time getting by when your car suddenly needs a $500 repair or you need a new furnace. You need to improve your cash flow so that you actually have discretionary income. Pay off those credit cards, then start directing those old payments into savings and investments.