Choosing a topic may seem like something quick and easy that you do before you get to the "real" research, but it's also a part of the research process. If you choose a topic thoughtfully, you'll have less of a chance of being frustrated and having to change your topic later.
The first thing you may wonder about your potential topic is whether or not your instructor will approve of it. The first place to look for information about this is the assignment itself. Are there are limitations placed on your topic? Are examples given of good topics, and what made them good topics? Look through the assignment thoroughly to understand your instructor's expectations. If you're still unsure, ask your instructor for clarification.
Once you have some topic ideas in mind, do a basic preliminary search. Make sure to search for the kinds of sources that will be required for the final project - for instance, if your assignment requires you to find academic sources, do your preliminary search in a library database. A basic Google search can get you started, but make sure to pay attention and see if the results Google brings back are ones appropriate for your assignment.
You don't have to try and find your final sources during this search. You're just trying to get the lay of the land. If you do an initial search and there isn't very much out there, it may be an indication that you need to adjust your topic. A large number of results with a lot of variety could show that you'll be able to thoroughly explore your topic, or possibly that you need to narrow it down. Looking at initial search results may also give you alternative topics - if there is a subtopic or a related topic that keeps coming up in your results more than your initial idea.
You will have an easier time of completing an assignment if you can connect to your own life and your own interests. Where is the overlap between what the assignment requires and what you are interested in? Resist the temptation to fall back on a "safe" topic that you have no investment in; this could make it harder to stay motivated. If you want assistance making connections between the assignment and your interests, consult your instructor and/or a librarian.
The following resources are ones you can browse in order to get ideas for a speech topic. Any topics you find in these resources should have at least a few sources supporting your topic to help you get thinking. Be aware that they are generally very broad - like "food" or "foreign policy" - and you'll probably want to narrow it down for your speech.