There is a lot of satisfadction in knowing that you have written a good essay. You feel better. You sleep better. And you probably got a good grade.
About the only way to write a good essay is to get something down on paper--a first draft--and then to go over it line by line and even word by word until you feel satisfied that it is coherent, persuasive, and smooth. You don't necessarily have to have a "good starter" when you write your first draft. A lot of students get hung up, and actually develop writer's block, because they think they need to write their thesis sentence or thesis paragraph first. Sometimes you get your best ideas for a thesis sentence while you are writing part of the body of the essay. A lot of times you find yourself writing things that surprise you. (Did that come out of me?) And your thesis statement might pop into your head while your writing your conclusion. I think it was Emerson who said that writing takes you where you didn't expect to go.
E. B. White talks about this in the last chapter of his The Elements of Style. He says that sometimes you have to cut your manuscript into pieces and spread them out on the floor to rearrange them. This was in the days before computers. Now you can have several separate sections in separate files and rearrange them with the word processor. James Thurber, who was a friend and associate of E. B. White and an equally good writer, said, "Don't get it right; get it written." He meant that you have to have something on paper before you can smooth and polish and perfect it.
A good essay doesn't come out all of one piece like something created by a zen master. Maybe after you've been writing for many years, and have one good day, you will turn out a good essay on the first draft. But in the meantime you have to get used to just saying the words and then letting them ferment for awhile, if you have the time and aren't pulling an all-nighter, and then rewriting and rearranging until you have something you're satisfied with.
You can think about your starter last, and just keep rewriting it until you think it's good. Writing is hard work, but that hard work pays off because it makes you a better writer and a better thinker.
I did not read billdelaney's responce so he may have mentioned this, but a simple good way to start an essay would be to ask an intriguing question. The question will act as the hook to get people to read on so make it a good one!