Well, hello Edward Ferrars!
In Chapter 3, we meet Fanny Dashwood's brother, Edward. As the eldest son, he is the heir presumptive. We already know that his mother is stingy, based on what Fanny said in chapter 2, and that she controls the purse strings - something that is repeated in this chapter, just so we don't forget about it. This means that Edward is likely to be well-off eventually, but also that he is likely to have to marry well, since his mother will have to approve the match. We're told that his mother and his sister both want him to make a splash, somehow earning a name for himself in politics or as one of the great men of the times. His sister's desire for him to have a barouche is a desire for him to engage in ostentatious display, since a barouche at the time was the equivalent of a luxury convertible now.
Edward is a nice, quiet guy who hits it off with Elinor, and they form an obvious emotional attachment. Mrs. Dashwood is only too happy to think of Elinor being married and settled, and it suits her romantic nature just fine to jump to conclusions as soon as Elinor says a favorable word about him. Marianne, who is still more romantic than her mother, is less certain that she approves Edward as a suitor. He's not sufficiently heroic for her - she wants a Mr. Darcy, and not Mr. Darcy the prig at the beginning of P&P, and probably not even Mr. Darcy at the end of P&P, but the Mr. Darcy everyone concocts for themselves, who is tall, dark, handsome, rich, well-educated, well-dressed, and refined, and also caring and exceedingly "into" his lady love. It is not enough that Edward approves Elinor's painting - Marianne believes he ought to know all about painting, and finds him deficient for saying nice things just because it was Elinor's artwork. Marianne complains about his flat reading of the poems of William Cowper (pronounced Cooper, incidentally), who is best known for his poem The Task and for " ". Marianne wants a far more dramatic rendition of the poem, you see.
You'll note that we don't learn what Elinor thinks of Edward in this chapter, apart from her observation that he's not at all like his sister - a big plus!
A few points
1. House visits in Austen's time sometimes lasted for months on end. A family visit such as this at a country house put everyone there in close proximity with one another. They would have seen each other at meals, spent most evenings together, often in a group activity such as a shared musical event (one or more persons played and sang for the group), reading aloud (from such things as religious tracts, Shakespeare, novels, poetry or one of the popular travelogues of the time), games of cards, chess, or backgammon, and so forth. Well-off gentry did not often engage in most household chores - they had servants to haul wood, fix fires, milk cows, work in the fields or forests, do the cleaning, cooking and laundry, etc. So they probably saw a good deal of one another during the days as well, when occupied reading books and newspapers, writing letters, talking a walk, riding horses, receiving visitors or paying visits to others.
All of Austen's original readership knew exactly what day-to-day life was like for the landed gentry, and all of them knew exactly how days among family were spent, and how likely it was that Edward and Elinor were spending a great deal of time together, whether they got along well or not. I mention it to you now, because it's something that we as modern readers often do not give much thought to, and since Austen does not relay all that many conversations between Elinor and Edward, it would be easy to assume that perhaps there's little on which to build a relationship. My point is that there is MUCH on which to build a relationship, but it's contained between the lines here.
2. We are quickly learning that Elinor is "sense" and Marianne is "sensibility" (a word which then had to do with emotion and feeling, and not with common sense). Elinor is practical about money where her mother is not, and she says "Edward seems nice", which is enough for her mother to declare that she will love him then, while Elinor charts a more measured path, saying that they should get to know him, and probably they will think well of him. Marianne has extreme opinions on Edward based on what little she's seen of him. She wants a man who possesses all of Edward's virtues (which includes goodness), but is also handsome and charming and polished.
3. Going forward, we'll be looking at this dichotomy between the sisters, as well as if, how or how much it changes. While this novel involves romances involving both sisters, Austen's choice of a title makes clear that she's looking specifically at these characteristics. And the original title of this novel, Elinor and Marianne, makes clear that the key relationship in this novel as far as Austen is concerned is the one between the sisters. This makes perfect sense, when one realizes that Austen had a sister named Cassandra who was three years older than she was, and that Austen and her sister were entirely devoted to one another, but of different temperaments.