The goals of your first paragraph should be (1) to communicate the thesis to the reader, and (2) to lead your reader to say, at the least, "this essay is a contender."
1. The thesis. Unlike an academic essay, sometimes the thesis of an admission essay does not assert an argumentative or aesthetic point. In many cases, it is a one-sentence summary of the overall topic of the essay. Moreover, the first sentence often can serve as the thesis.
Take, for example, the line above about rowing on Lake Bled. If the point of the essay is to describe the joys of the best day of your summer vacation, the words "I was enjoying the best day of my summer vacation" explicitly give the message of the essay. On the one hand, this message would fall short in an academic essay, because all you're doing is telling a story. True, you will be presenting evidence to support the thesis, but what's academically interesting about your great day? On the other hand, providing a message about what you value is just the kind of action that admission officers want you to perform.
But you could just as well take the admission essay in an interesting, more academic direction. Maybe the greatness of the day is just a backdrop for your real point: Lake Bled is so great because it hasn't been commercialized into a "tourist attraction." Your thesis could be something like, "The best part of my experience was the solitude, the feeling that I could enjoy the whole day without the presence of car horns, ice cream vendors, or tourists wearing 'Lake Bled' T-shirts." Or you could use that sentence to lead into an explicit thesis on the same topic: "I felt fortunate that Lake Bled is so much unlike 'tourist attractions' back home."
2. Becoming a Contender. In addition to choosing a meaningful topic and constructing a terrific first sentence, developing a crisp opening paragraph can impress your readers. This requires some ruthless cutting and perceptive editing.
The shortest opening paragraph could be just one line of dialogue. In a narrative essay, occasionally a one-sentence opening paragraph can be effective. The shortest standard opening, however, is no shorter than three fairly short sentences. Beyond that, you could go up to eight sentences if you have, say, a two-page personal statement to write. But most uninspiring essays are top-heavy: they are too bulky in the first paragraph, so the reader has to wade through too much material before getting to the point. Here are two ways to keep your opening crisp:
a. Classify the information in the first paragraph into either "explanatory" or "introductory" material, and then move all the explanatory material elsewhere in the essay. The introduction is for introducing, not explaining.
b. Commit, at least for now, to cutting the paragraph by half. It won't be enough just to improve the style and "tighten up" each sentence; some sentences will have to go. Identify the weakest sentence, and cut it. Then cut the next weakest sentence. Maybe you can save a phrase by incorporating it elsewhere in the paragraph, but the rest of the sentence can go. Keep going until it really would feel quite painful to cut further. As you cut, think about what each sentence actually accomplishes for you and for the essay, and if it doesn't pull enough weight, wave it goodbye.
