Debt payments are usually the most onerous bill a person can be greeted with each month. The process of chipping away at a student loan, car loan, or credit card can seem neverending. You'll knock down some of the principal each time, but always lose a fair amount of money to interest.

Debt payments can be particulary concering if you're looking to buy a home, since you'll have to save up a healthy amount of money to make as a down payment. It is often recommended that you have at least 20 percent of the home's price available for a down payment to avoid mortgage insurance costs, although options are also available to purchase a home with less money down.

Unfortunately, with all the other financial obligations you regularly face—food, utilities, putting away money for retirement—it can be difficult to both pay down your debts and save up for a home. Though your strategy will depend on your own personal situation, it sometimes makes the most sense to focus on one goal before attempting the other.

Many debts come with interest rates that are far higher than what you could realize in a savings account. Therefore, you'll save more money in the long term if you pay these debts down first before focusing on saving. Erik Carter, writing for Forbes, says you'll save more in interest if you pay down any debts with an interest rate higher than 7 percent.

If you have multiple debts, focusing on the one with the highest interest rate will result in the most savings in the long run. However, the University Federal Credit Union of Austin, Texas, says paying off a smaller loan might give you a psychological edge simply by relieving you of some of your financial obligations. It also frees up those payments to attack other debts.

You can also try to modify your debt so that you have an easier time paying them off. These options include consolidating loans, transferring credit card balance to the card with the lowest interest rate, and simply limiting the amount of spending you do with a credit card.

Paying down debt will improve your credit score and put you in a better position when you visit a lender for a home loan. However, putting your credit card debt onto one card can harm your credit score. Michele Lerner, writing for the National Association of Realtors,  says closing a line of credit will also lower this score by shortening your credit history. By having less debt, you'll also be in a better position when the lender calculates the debt-to-income ratio in determining what kind of mortgage you can afford.

Having some savings on hand is a big advantage, however. Building up a small emergency savings account will give you a nest egg to meet any unexpected expenses. The University Federal Credit Union says that without this fund, you'll simply increase your debt by having to rely on a credit card. A balance of at least $1,000 is enough to meet many crises.

You should also work to build up enough money to cover your regular expenses for a period of three to eight months before you take on your debt. Carter says this boosts the emergency fund to a level where you will be able to meet regular expenses if you lose your job, are ill for a long period of time, or otherwise lose your earning capacity.

There are also some disadvantages to focusing on your debt payments without building up any savings when it comes to buying a home. Lerner says that if you dip into existing savings, you'll reduce the amount you're able to contribute to a down payment. She says the best time to pay off your debt is when you will have enough left over for a down payment, emergency expenses, and closing costs.

If you are paying a low interest rate on a debt, it is a less pressing concern. Carter says that if the rate is below 5 percent, you'll realize more benefits by maintaining modest payments on this debt and investing the extra money in savings.

It sometimes makes the most sense to strike a balance between reducing debt and increasing savings by making steady payments to each. Doing so will allow you to build up money toward a down payment right away instead of starting once you have eliminated other debts, allowing you to purchase a home sooner.