It is quite true that Shirley Jackson selects characters and language that are simple and easy to relate to. That is precisely the reason behind it: Because the theme of "The Lottery" is about the very complex tendency of human beings to follow traditions without questioning their purpose or rationale. As a result, we become victimized by our own beliefs and make others victims as well.
The complexity of this topic is easier to treat and expand with characters that are simple and to which the audience may find it easier to connect. In "The Lottery" we have such characters. There is Mr. Graves, the postmaster, Mr. Martin, the grocer, Tessie, Mrs. Graves, and Mrs. Adams, who are housewives, their husbands and children. All of these seemingly normal people are part of the biggest irony: They have a deadly ritual that they practice without question. In it, they stone the "lucky" person whose name is drawn after a complicated and ancient process of drawings is conducted.
Added to the morbidity of the action comes the contrasting nature of the narrative, for all of this happens in a normal, and beautiful day
The morning of June 27th was clear and sunny, with the fresh warmth of a full-summer day; the flowers were blossoming profusely and the grass was richly green.
Here we see the sick irony of it all: Along with the natural view of the day, we see that, hours later, there will be the "everyday" grocer holding the lottery box while the town's postmaster administers it. Meanwhile the entire town will stop their everyday activities and get together to celebrate this tradition.
The people of the village began to gather in the square, between the post office and the bank, around ten o'clock; in some towns there were so many people that the lottery took two days and had to be started on June 2th. but in this village, where there were only about three hundred people, the whole lottery took less than two hours, so it could begin at ten o'clock in the morning and still be through in time to allow the villagers to get home for noon dinner.
All of this becomes twice as macabre with the simplicity of the narrative and the relative normality of the town and its people. The contradictory nature of the dynamics and their purpose make for a very shocking ending and a much more interesting read.
The irony in Jackson's "The Lottery" is that the author and characters know far more about what is going on than the reader does, and as your question implies, we are set up for a relatively horrible surprise by the setting--a peaceful agricultural town on what appears to be a typical summer market day--and salt-of-the earth characters who are doing their marketing and catching up on gossip. We know they are there for a lottery, but both the setting and the characters create expectations of the kind of lotteries we understand:
Soon the men began to gather, surveying their own children, speaking of planting and rain, tractors and taxes. They stood together, away from the pile of stones in the corner. . . .
Other than the pile of stones, which could be used for many purposes in an agricultural community, all is as it should be: small conversations among farming people about universal concerns--weather, machinery and taxes.
A few lines later, we learn that
The lottery was conducted--as were square dances, the teen club, the Halloween program--by Mr. Summers, who had time and energy to devote to civic activities.
Again, our expectations are confirmed that the lottery is no different from any other "civic activities," and it is lumped into such harmless activities as square dances and "the Halloween program," thereby lulling us into the belief that the lottery is simply another celebratory event in this typical American farming community.
Jackson did provide elements of foreshadowing, but like the foreshadowing in Faulkner's "A Rose for Emily," we recognize those elements only in hindsight. These elements include the pile of stones that the men do not stand next to; the color of the lottery box is black, and when Mr. Summers needs help setting it up, his helpers seem to hesitate; and every member of the community, to the youngest child, has his or her name in the lottery. Even with these clues, our expectations are not ready to be flipped upside down.
When we read most literary works, we know at least as much as the narrator, perhaps a more, and it is relatively rare to experience the irony of having the narrator and characters know so much more than we do. Jackson does a superb job of molding our expectations in such a way that we are (unless some of us have flipped to the end) shocked, stunned, when we realize that the purpose of this lottery is to sacrifice a life in such a horrific manner, ostensibly for the greater good of the community.