The final answer comes down to you - your personality, what makes you tick - and whether debt-free living is your dream. If being free of debt sets you free, then committing yourself to it should indeed be your priority. The one thing that almost all advisors seem to agree on in this context is to get out of one of your highest-interest rate debts - your credit cards. Before you tackle your student debt, car loan, your home mortgage, or any other debt, take care of your credit card debts. These debts are unsecured, and hence carry high interest rates, and are often a reflection of poor money management habits on your part.
The first step towards freedom from credit card debts is to control spending. Often, just as many of us use food as our emotional balancer, shopping and spending money gives many that same emotional satisfaction (retail therapy). The best way to break that pattern is to observe it - like a neutral observer, even as, mechanically, you open your purse or wallet and buy something that gives you that quiet feeling of satisfaction. Observing the pattern will eventually break the pattern, as a higher intelligence (that is You in an aware and awake state) see the pattern for what it is, and realize that it does not get you any closer to where you want to be, in spite of the short-term relief it brings.
Once your spending is under control, half the battle is won! Now pick one credit card, and start paying it down, until it is completely paid off. Both Suze Orman and Dave Ramsey recommend this approach, though with slightly different twists. Pick off your credit cards one after the other, until you are completely clear off all your credit card debts. Suddenly, with your spending in check, and your credit card debts paid off, you will find yourself with plenty of extra cash left at the end of the month. We do recommend paying off your car loans and student loans next, leaving you only with mortgage payments.
Thus, from any given situation, with determination and commitment, you can chart out a 7-10 year plan that will bring you to a debt-free state and help you begin enjoying a debt-free life!