The first chapter gives us a list of many of the principal characters in the book, some of whom we don't truly meet here. In fact, we really only see into the minds of the foolish Sir Walter Elliot and his equally foolish daughter, Elizabeth, who, being the eldest unmarried female child, is called "Miss Elliot" when in society.
Sir Walter Elliot
Unlike her previous book, Emma, which began with a brisk description of the main character, this book begins more in the vein of a much earlier composition, Pride and Prejudice, with an introduction to a foolish parent: in this case, it's Sir Walter Elliot, who is quickly and clearly established within the lengthy first sentence as a vain and silly member of the landed gentry. He is a baronet, which is a hereditary title, passed to the eldest male heir from generation to generation; it is not, however, actual aristocracy, but a title that was conveyed to an ancestor in exchange for large donations to the royal coffers. To be so puffed up over a title that is not actually a truly noble one marks Sir Walter Elliot as a fool, something that Austen's initial readers (with their knowledge of titles and status) would have immediately seized upon.
Sir Walter is a widower, the father of three daughters, who lives at Kellynch Hall, an estate in Somersetshire that is, like that of Mr. Bennet's in Pride & Prejudice or the elder Mr. Dashwood in Sense & Sensibility, tied up in such a way that it cannot be divided up. Unlike Mr. Bennet, Sir Walter has the ability to sell the estate, but he would have to sell the complete parcel, something his pride will not allow him to do. The importance of Kellynch Hall is emphasized not only by its placement early on in the first sentence, but in the number of times the its name is repeated in the first page. The importance of the estate to the Elliot family cannot be trivialized: it is a source of pride, certainly, but also of income and sustenance. We learn rather rapidly that Sir Walter has grossly exceeded his means and needs to find some way to economize or risk financial ruin, which necessitates him leasing his estate to someone else for the time being as a means of increasing his own income through rent payments while also reducing his expenses - he will need fewer servants at a house in Bath. The issue of to whom he will lease the estate reveals Sir Walter's petty nature, but also makes clear that Austen is not opposed to the idea of a meritocracy, where one might be upwardly mobile by proving their worth, rather than by having an inheritance.
William Walter Elliot, Esquire
We don't actually meet Mr. Elliot in person until much later in the novel, but he and his existence hang over the Elliots of Kellynch Hall from the get-go. He is a cousin (removed a bit), and the closest male relative. We need know nothing more about him until later, except that he is an attorney, and that he and Sir Walter have had a falling out because the younger Mr. Elliot married a wealthy young woman instead of Elizabeth, Sir Walter's eldest daughter.
Lady Russell was the close friend of Mrs. Elliot. Mrs Elliot died when Anne, our main character, was only 14 years old. She has been a trusted friend of the family ever since. She did not remarry after the death of her husband, which Austen explains as follows:
That Lady Russell, of steady age and character, and extremely well provided for, should have no thought of a second marriage, needs no apology to the public, which is rather apt to be unreasonably discontented when a woman does marry again, than when she does not[.]
Eldest daughter and "lady of the house" since the age of 16. Her personality is quite similar to that of her father's, and she is similarly vain and of a superficial nature, and similarly disinterested in the practicalities of life. Elizabeth's idea of economising is to cut off her charities, hold off on redecorating the drawing room, and to not purchase a gift for Anne when she and her father were living the high life in London. Elizabeth had once been quite the eligible beauty, but never married. She is now 29 years old, which essentially puts her "on the shelf", although she seems rather unaware of that being her position. She is nevertheless quite bitter about Mr. Elliot's disinterest in courting her when she was younger, and quite disinterested in renewing her acquaintance with the now-widowed Mr. Elliot.
Mary Elliot Musgrove
Mary, the youngest of the three girls, is the only one to have married. She is married to Charles Musgrove, eldest son of a neighboring gentleman landowner who stands to inherit the estate of Uppercross when his father dies. We will learn far more about her in chapters to come, but suffice it to say that she eclipses even Mrs. Bennet from Pride & Prejudice when it comes to comic hypochondria.
We come at last to an extremely slight description of Anne Elliot, our main character. Anne is now 27, and still single. She was once pretty, although her beauty was never valued by her father or elder sister, but is acknowledged as a woman of superior value by people with actual taste. She is a reliable, practical young woman who was once very much in love with a young sailor, although we do not find out that last bit of information for another several chapters.
Mr. Shepherd is Mr. Elliot's agent - a gentleman, although not of any real rank, who is charged with overseeing Mr. Elliot's accounts.
On to the next chapter.