Good ways to start an essay are to use:
a real-life story from the news or history
a story from your own life or someone you know (a personal story)
a story from fiction, T.V., or a movie
an example of a typical situation which illustrates the problem or situation you are talking about
a conversation between two people about the issue (real or made up)
facts that everyone knows about the situation
statistics about the situation
an explanation of the problem
more than one of the above.
For example, I often suggest that students start with a personal example of the situation to draw in the reader's attention and then have them give statistics to show the scope of the problem. With any of these examples, you can still use the sentence starters in this article to make your sentences pop out.