Okay, so you are trying to persuade the reader that the text of Lord of the Flies supports the assertion that "man's nature is basically evil and selfish?" Than what you need are examples from the text that would help support this assertion. We will look for examples of characters acting in immoral or selfish ways. Luckily, that's not too hard to find in LOTF:
“They used to call me Piggy.” Ralph shrieked with laughter. He jumped up. “Piggy! Piggy!” “Ralph—please!” Piggy clasped his hands in apprehension. “I said I didn’t want—” “Piggy! Piggy!”... “You’re talking too much,” said Jack Merridew. “Shut up, Fatty.” Laughter arose. “He’s not Fatty,” cried Ralph, “his real name’s Piggy!”
Here we see Ralph and Jack making fun of "Piggy's" weight.
“His specs–use them as burning glasses!” Piggy was surrounded before he could back away. “Here–let me go!” His voice rose to a shriek of terror as Jack snatched the glasses off his face. “Mind out! Give ’em back! I can hardly see! You’ll break the conch!” Ralph elbowed him to the side and knelt by the pile.
Again, here they are taking on poor Piggy. The rudely snatch his glasses and push him aside. Their desire to start the fire has overwhelmed their interest in civility.
Roger and Maurice came out of the forest. They were relieved from duty at the fire and had come down for a swim. Roger led the way straight through the castles, kicking them over, burying the flowers, scattering the chosen stones. Maurice followed, laughing, and added to the destruction.
In this section, we see the bigger boys coming out of the woods and smashing the sand castles and hard work of the littluns, laughing while they do it. This seems to support your ideas about "evil."
“Kill the pig. Cut her throat. Spill her blood.”
This quote is pretty much self-explanatory when it comes to your thesis.
Ralph made a step forward and Jack smacked Piggy’s head. Piggy’s glasses flew off and tinkled on the rocks. Piggy cried out in terror: “My specs!”
Poor Piggy gets it again. They don't care that he can't see squat without those glasses. This is the beginning of actual physical acts of violence between the boys.
“The rules!” shouted Ralph. “You’re breaking the rules!” Jack: “Who cares?”
Later, Jack says:
“We don’t need the conch any more. We know who ought to say things. What good did Simon do speaking, or Bill, or Walter? It’s time some people knew they’ve got to keep quiet and leave deciding things to the rest of us.”
Here's the breakdown of the rules. Humanity can only hide under the veneer of civilization for so long before breaking apart.
That's enough, I think, for you to see the kinds of things you are looking for. I left the more obvious ones from the end of the book for you to dig out yourself: Piggy getting killed, the boys hunting Ralph, the island essentially being destroyed in a rage of fire.