If this essay is to be argumentative, you may wish to pick a side in the issue to begin with. For instance, if you are in favor of increased government spending to handle the homelessness problem, a potential topic sentence may be, "There are many reasons why our government should spend more to address the rampant problem of homelessness."
Likewise, if you believe that homelessness is largely a result of one's own choices and that government should decrease its interest in the matter, a potential topic sentence might be something like, "While homelessness is a social issue affecting many people, there are many other more important matters that our government should focus on instead."
Such a sentence would then allow you to elaborate on what those other areas are, and why they should take precedence over the plight of the homeless.
Because this is a research paper, you may wish to seek out statistics and facts that help substantiate your point. If you feel the government should increase its spending on the homeless problem, what are some numbers that indicate how big the problem is? Likewise, if you feel that our focus should be on other social and political matters, what are some statistics that help bear out that opinion? You may wish to examine this matter from "both sides of the aisle," so to speak, but make sure you choose one good point to hammer home as the thesis statement of your paper.