A topic sentence is one of the most popular ways of opening the first body paragraph. Typically, the topic sentence corresponds to one of the points in the thesis statement. For example, if your thesis statement reads, "Because of reason X, Y and Z, alternative medicine is fundamentally flawed," your first body paragraph could read, "Reason X is a big part of why alternative medicine will prove unsuccessful."
A transition sentence is a great way to open the first body paragraph in a paper. Transition sentences establish logical links between different ideas. For example, if your introduction ended with a thesis statement about how the author establishes setting, you could start the first body paragraph with a sentence like, "The first way the author establishes setting is through..." This phrasing creates a transition between the first body paragraph and the intro, because it flows naturally from the last sentence in the thesis statement.
The first body paragraph is also a good place to define key terms in the paper. In a traditional five paragraph essay, this can be hard to do, because every body paragraph is supposed to do the same thing for a different argument. However, in more advanced papers, which do not demand such a symmetrical style, it is possible to use the first body paragraph primarily to define key terms. For example, if your paper deals with a technical topic like economics, you can open the first body paragraph by saying, "Before we can speak of economics, we must define supply and demand."
If you are writing a paper based on a case study, it is a good idea to use the first paragraph to summarize the case in question. For example, if your paper is based on a crime report, you would use the first paragraph to summarize the facts of the case. If you are using the first body paragraph in this way, it is good to open the paragraph by describing the nature of the facts. For example, if the facts in question are contradictory, you could open by saying, "The facts in the John Doe murder case paint a complex and paradoxical picture."