The initial paragraph or first few sentences are the second decision point for a reader (and, I'm afraid, many editors). The story introduction has several duties.
- It needs to convey the style and tone of the story. -Elegant, musical prose can be a joy to read in itself. -Genre specific phrasing sets the reader's expectations. -Staccato words can tell the reader to get ready for action. This doesn't mean you should change your style - just be aware of it. Think of the first paragraph as the movie trailer; you are not giving a synopsis, but you are opening the toga.
- A plot point that grabs the reader's interest in "What's next?" is invaluable.
- Tell the reader this is going to be easy and fun. For most people, a short story is read for enjoyment. It is not wading through an analysis of the rise of China or going brain dead over Biology 410. If you're going to make the reader think (which most good short stories do), wait till the story gets going.
- Connect with the reader. This can be done a ton of ways, but generically, it is often by revealing a bit about a character or the world a character lives in. Stories are all, in one way or another, about people and their emotions.
You don't have to do all these things, but you need to consciously be aware of what you want the beginning paragraph to achieve and make sure it does. Remember, the reader has not read your story yet; all they have to evaluate so far is these few precious words.