Possible topics would include questions such as some of the ones we have examined in class: What is the nature of reality? Which metaphysical theory best explains reality (dualism, materialism, etc.)? What is the basis for ethical decision making? How do we know anything? Arguments for or against believing in god.
Or, you might choose a specific issue relating to ethics or political philosophy. Such as examining the strengths and weaknesses of utilitarianism; offering an analysis and potential solutions to the problem of evil; do people have a natural right to privacy? Which is more important, the common good or individual freedom? Why?
Which regard to these topics, you should identify the problem or issue, then engage that issue using the claims of one or more philosophers who have offered their views on that particular issue. You might compare and contrast two or more philosophers on a specific issue.
Another option would be to research a specific philosopher answering such questions as: what problem or problems were they trying to resolve? What factors explain their positions? If applicable, how did they respond to their opponents?https://en.wikipedia.org/wiki/Utilitarianism