I think this question relies greatly on an individual's tolerance for risk, as well as several other factors not mentioned.
What is the interest rate on those student loans? Will you have potential for higher earnings in the future or are you on fixed salaries? How long did it take you to save that $24,000?
Without those questions answered here is my two cents. Personally, I won't pay down debt that is less than 5.5%, mortgage related or otherwise. My situation is somewhat different from yours, but that is my opinion. You are better off doing pretty much anything else with the money if the interest is below 5.5%. As the interest rate gets above that, you may still be better off using that money as a down payment for a rental or stock related investments, but it becomes much riskier.
With your current income situation, I would try to get my hands on a rental. It is difficult to save that amount of money and you likely don't know how long it will take you to save that amount of money again. Even just one rental could make a huge difference in your lives. Not only will it hopefully provide some cashflow, but more importantly it allows you to begin building wealth in an asset class that very few people at your income level are involved in. In the long run, even just one additional rental that you own outright could make a huge difference to your quality of life and position financially. Not everyone needs to be a Brandon Turner.
That being said, I live in a lower cost of living area, and 24k is enough for two down payments, whereas you may not even be able to afford one. If that's the case, I might try to get an FHA loan by finding a deal you can house hack, or try investing in a nearby, lower price point area.
All of this is simply what I would do, whatever you choose to do, best of luck to you and your wife!