I'm not a financial adviser, but I have around 20 years experience in trying to pay off my own debt. This is my advice based on my own experience and knowledge gained the hard way.
I agree with what most of the other answers say, but there is something else to consider that no one else (so far) has mentioned: your credit score/report.
Because of this, I disagree with the order @Harper says to generally pay off loans to the point where I believe his order is exactly reverse.
Pay off the unsecured debt first, then the secured debt, then student loans.
Having unsecured debt collectors come after you drains your bank and your paycheck to the point where you might feel the need to start more unsecured debt to "get out of the hole." Unfortunately, that's only putting you farther in. So is using paycheck lending services. The rates they charge you are often equivalent to a 1200% interest rate or more.
Secured debt collectors will take your stuff, but will tend to leave your cash alone. It's a bitc-, um, PITA, but you can find a cheaper car to drive or house/apartment to live in.
Student loan companies will call you incessantly, but they are willing to work with you. If they are federal loans, they might take your tax refund, but I've been so far behind on payment it wasn't even funny and they still didn't do anything besides call every day. I've even had them basically give up calling me for a while. It's not the best situation, but you aren't likely to see anything serious from them.
Near the end of that article, Barry Paperno states:
The most critical scoring distinction between cards and loans tends to be within the amounts-owed category, where loan debt carries far less scoring weight than credit card debt, which includes credit utilization and some other debt-measuring calculations. For this reason, if you ever want to help your score by paying down some of your debt above and beyond the minimum payment, always pay your credit card balances before any loan debt.
Also, student loans can be deferred if you lose you job, and there are other things they can do in times of economic hardships. They can reduce your monthly payment to nearly nothing, while you maintain your good credit standing.
As with most other loans, you can give your credit score the biggest boost by making your student loan payments on time. It's worth noting that student loans are typically treated as installment plans by the three major credit bureaus...
Opting to defer on student loans, while not as ideal as repaying them because it simply delays the inevitable, won't hurt your credit score.
It also says:
In (U.S.) states where it is legal, employers may even check a job applicant's credit report before making a final job offer.
This means that if you lose your job, you might have a hard time getting another one, while having lots of debt. This is especially true if you work in retail, where you may handle money all the time. I've heard that register clerks are the biggest target for a credit check before hiring.
I agree with the need for an emergency fund and will suggest that it's more than just an "I'm unemployed" backup. As stated previously, it should b 6-8 months of bills, to include food and fuel. I'm going to say that's the minimum you should have saved, and you should have more ready for car, home, appliance, and other repair/replacement needs. I've gotten myself into trouble by paying my bills, only to need to figure out how to fix my car(s) the following week.
Your savings should be your "goto" for all emergencies, not your credit cards. Credit cards aren't evil, but they can get you into deep shi-, um, manure. Credit cards should only be there for extreme emergencies, where your savings just can't cover it all. They aren't usually used that way, but that's a different topic. However, if you pay off the credit card each month, before interest is applied, you can get away with using them to help boost your credit score. It's tough to maintain that discipline, with one misstep getting you interest charges, and more missteps causing you more problems. Again, most people aren't using them this way.
Now, back to the money bit you actually asked about.
Interest that you pay is your enemy. As others have done the math, I won't. Also, I agree with the snowball effect as well as paying off the largest interest rate first, and these coincide in your case, so there's not really much else to say.
Pay off the two high interest loans first. That leaves you $1238.45. Keep it as a start for your emergency fund. If you feel you need to put some towards the 3rd amount, put only $250-500 towards it.
You still want to pay that $9,584.80 off, so here's how to do it the "right way."
You just zeroed out 2 loans that gain you $280.21 worth of your monthly paycheck back into your pocket. Use part of that to roll into paying this loan. I'm going to suggest splitting it down the middle so you put $140.10 more each month toward the loan and $140.10 goes into your savings/emergency fund. (There's 1 penny left that you can just keep in your checking account.)
After a year, you'll have put almost $1700 in your savings account from your wage (plus whatever you kept from the $1238.45) and have paid that much extra to your loan. This is a great start. If you continue doing this, you'll have that 3rd loan paid off in under 2 years.
After that 2 years, you could have just over $4600 in savings. I've paid less than that for 3 out of the only 4 cars I've owned. Now you can save even more, since you have paid off that 3rd loan and can add another almost $500 a month to your savings. That's another $6000 a year you are saving at that point. That is, if those are your only 3 loans, which I suspect isn't the case, and you're "the average American."
After saying all that, you are going to pick whatever method you like best. So...
Good luck and I hope things work out for you!
@quid, bankruptcy should always be used as an absolute last resort. It stays on your credit report for 7 years, and it can block you from buying a house or car. Some lenders will still loan you money with a bankruptcy, but at very high interest rate, so you're likely to get back to where you were before the bankruptcy. Also, bankruptcy isn't always an option. Having less than $10k in unsecured debt usually doesn't let you have that option, and some people think it's a huge stigma against them, which will cause them mental pain not worth the financial savings.
I've been at the point where my bank account, then my wages, were garnished for $2500 debt. Bankruptcy wasn't an option and it wouldn't really have helped, since I had tens of thousands of student loans that wouldn't have been affected, which were most of the problem anyway. Also, a judge can decline the bankruptcy, so now you have the legal bills to also cover. The judge can also rule that you have to drain your bank to try to repay the loan before the rest is decided, and again the judge can decide what debt to wipe out.
Regardless of what you hear about Trump's bankruptcy's, it's not the magic "get out of jail free" card most people seem to think it is.