The opening of Pride and Prejudice is a complex one and one that is ofttimes misunderstood. This elusiveness of understanding is complicated by film versions of the novel that compound the misunderstandings of Austen's opening.
The difficulties begin with the tone of the narrator. Austen famously employs a narratorial voice that is close in proximity, subjective and wittily ironic. This intrusive narratorial mode can create difficulties if not read with an eye to clues in grammar and vocabulary that open a correct understanding of what or who is being commented upon or described.
Let's look at Mrs. Bennet since Austen begins with her. Mrs. and Mr. Bennet begin the novel, with only indirect reference to the principal characters of Elizabeth and Jane (the daughters are introduced in Chapter 2), in order to embed the story within the elements that lead to Darcy's objections to the Bennet family of Longbourn: Mrs. Bennet's small-mindedness and unpolished manners, which we find infect the manners of three of her five girls, and Mr. Bennet's neglectful management of his family.
One misunderstanding that arises from this ironical opening is that the Bennets have a "middle class" social station. This is not true. Mr. Bennet is in the same class as Mr. Bingley and Mr. Darcy: all three are gentlemen of independent wealth. Thus all three are in the upper class. The differences between the three upper class men is that (1) Darcy's wealth is attached to a country estate and both are inherited through many generations; (2) Bingley's wealth is newly built by his industrialist father, and Bingley is the first to inherit it; (3) Mr. Bennet's wealth is also attached to a country estate but he has foolishly spent more than he has inherited in capital.
The definition of upper class in Austen's time period included nobility, like lady Catherine de Bourgh, landed gentlemen of large fortune, like Darcy and (foolish) Bennet, and men who had amassed a large fortune through business of some sort, like the Bingleys. By English custom and law, all in the upper class were equals and entitled to marry without social stigma. This is why Elizabeth has the effrontery to contradict Lady de Bourgh with the statement that she and Darcy are equals: "In marrying your nephew, I should not consider myself as quitting [my social] sphere. He is a gentleman; I am a gentleman's daughter; so far we are equal" (Ch 56).
Mr. Bennet married for beauty. Mrs. Bennet, who was once Miss Gardner, was beautiful, vivacious, fun and charming. She was, however, the daughter of a man from the second social tier: Mr. Bennet married beneath is own social class. Darcy and Lady de Bourgh object to Mrs. Bennet's "connections." She has a brother, Mr. Gardner, who is in business and lives in an unfashionable area of London. She has a sister, Mrs. Philips, who married a country lawyer and lives in Meryton. Mrs. Bennet's manners and those of Mrs. Philips are exemplary of their class connections: they are unpolished though Mrs. Bennet's are also pretentious. The manners and deportment of Mr. and Mrs. Gardner present a happy contrast to the social coarseness of the Gardner women, Mrs. Bennet and Mrs. Philips.
So while Mr. Bennet married below his station, and that the Bennet connections are inferior, and that Mrs. Bennet is of lower class, the Bennets are definitely upper class. If this were not so, Elizabeth could not have dared to contradict Lady de Bourgh. Thus it is equally untrue to say that Mrs. and/or Mr. Bennet were intent upon having their daughters marry above their station: they are upper class; they can marry no higher than the upper class (although they might exceed all expectations and marry nobility, though this would be improbable).
Another misunderstanding concerns the portrayal of Mrs. Bennet. While she is portrayed by the narrator as "a woman of mean understanding, little information, and uncertain temper" who is "discontented" and narrow-minded, she is not portrayed as a working farm-wife who has no understanding of society's regulating manners. On the contrary, she is portrayed as a woman of great pride who is above doing any home- or farm-work and who is above the social restraints that regulate lesser individuals.
[Mrs. Bennet] assured [Collins] with some asperity that they were very well able to keep a good cook, and that her daughters had nothing to do in the kitchen.
This pride of hers is what compels her to act so boorishly in public: she fancies herself above and superior to all others in her neighborhood, including newcomers. In short, she fancies herself a local "Lady de Bourgh" in matter of consequence. Thus Mrs. Bennet isn't an overworked frump; she is a lady who believes her consequence, on account of marrying an upper class gentleman, is far greater than anyone else sees it to be. She is limited by her own "mean understanding" and prideful, shallow narrow-mindedness.
[Mrs. Bennet's] mind was less difficult to develop. She was a woman of mean understanding, little information, and uncertain temper. When she was discontented, she fancied herself nervous. The business of her life was to get her daughters married; its solace was visiting and news.
Another misunderstanding that can arise relates to the dynamic between Mrs. and Mr. Bennet in relation to her opening discourse with Mr. Bennet in which she request that he go visit Mr. Bingley when he arrives at Netherfield. She is not initiating a new or controversial idea in so requesting. It is Mr. Bennet's social obligation to call upon and open social relations with any single man who moves into the neighborhood. This is why he asks if Mr. Bingley is married or single: "Is he married or single?" If he were married, then Mrs. Bennet might initiate social contact by visiting the wife. Mrs. Bennet does not "push" Mr. Bennet into doing something that is out of the ordinary, she merely reminds him of his social duty; she has no reason to expect that he might refuse.
However, Mrs. Bennet does not understand the dissatisfied, satirical, ironical turn of her husband's disappointed mind, a turn that impels him to tease her and undermine her expectations at every opportunity:
Mr. Bennet was so odd a mixture of quick parts, sarcastic humour, reserve, and caprice, .... [He] was among the earliest of those who waited on Mr. Bingley. He had always intended to visit him,....
Thus, it must said that when Mrs. Bennet confidently reminded Mr. Bennet of his social obligation to his wife, daughters and neighbors, she was shocked to hear of his reticence to fulfill that obligation and felt forced to cajole him into cooperation.
[Mrs. Bennet said], "But consider your daughters. Only think what an establishment it would be for one of them. Sir William and Lady Lucas are determined to go, merely on that account, for in general, you know, they visit no newcomers. Indeed you must go, for it will be impossible for us to visit him if you do not." [...] Mr. Bennet was among the earliest of those who waited on Mr. Bingley. He had always intended to visit him, though to the last always assuring his wife that he should not go; and till the evening after the visit was paid she had no knowledge of it.