Welcome to Barton Cottage! Which turns out to be a tidy, regular little house that sounds remarkably like what we might call a center-hall colonial. There are two sitting rooms, one to either side, and behind them "the offices," a word which here refers to the kitchen and other rooms used by the servants in order to run the household – probably a butler's pantry and a storeroom, at the very least. Remember, they didn't have refrigeration then, so some meats were dried and hung, and things like cakes and the like were put into a cool place to keep them fresh.
I will note that it's possible that they had some cooling system on the premises, even in that time. For instance, if there were a spring on the property, they might have a spring house in which they could keep things cool via spring water. Or if they were near a stream or lake, they might have a building in which they had stored ice harvested from the local body of water in winter. In a temperate year, the ice could last into autumn. But at this point, I'm starting to feel like I've gone far astray from our story, so I return you to Barton Cottage: a neat, tidy, modern-for-the-times house, rather than a quaint, irregular structure with green shingles and a patched roof. It's well-situated on a hillside overlooking a valley, and the description of the house's position comports well with Gilpin's idea of the picturesque. (I don't recall if Gilpin is mentioned in S&S, but he's definitely mentioned or alluded to in Pride & Prejudice, Northanger Abbey, Persuasion and Mansfield Park.)
Despite how the house has been portrayed in the two most recent filmed versions (Emma Thompson's 1995 production and the 2008 BBC miniseries), the house is not isolated – in fact, they can see the village of Barton from one side of their cottage. And despite the Thompson movie's assertions to the contrary, Marianne has a pianoforte from day one at their new home, her own instrument having been sent on ahead for her.
Mrs. Dashwood – bless her – immediately starts planning a number of costly improvements to the cottage, including rearranging the walls on the first floor and building an entire addition so as to add a dining room downstairs and another bedroom upstairs. She is wise enough to defer any such alterations until spring, however. You'll notice immediately that it is now September, which means that the Dashwoods spent 6 months living at Norland with John & Fanny, and at least 4 of those months included Edward Ferrars staying there as well. (I mention this because we won't be seeing much of Edward for a while, I'm afraid, and oftentimes people assume that there's not all that much of an acquaintance between him and Elinor, when in reality they spent nearly all day every day together for months on end.)
The next day, we meet one of the most affable characters in all of Austen, Sir John Middleton, who is described as a good-looking man of 40 (although he is not usually cast that way in the films, but I digress). This distant cousin feels more actual concern and solicitude for them than Mr. John Dashwood ever did (even on a good day), and it is terribly hard for readers not to like him immediately. It is worth noting, however, that he can be a bit overbearing and/or overexuberant in expressing himself, which sometimes becomes a bit much for the Dashwood ladies. I'm sure you know the type yourself – that kind-hearted soul who asks too many personal questions or urges second helpings and then forces you to take leftovers home when you'd rather not? We've all met some equivalent, is what I'm saying. And they are harder to be charmed by in real life, even though our knowing someone like that in real life is what helps us to find affection for Sir John.
Sir John operates out of a place of extreme good-heartedness, however, and has a desire to be useful. And thus it is that after riding over to meet them in the morning, he immediately sends over a large basket of fruits and vegetables from his garden, and later in the day has someone deliver them some game (likely rabbits or birds) so that they have provisions for their meals. Knowing they have no horse of their own, he offers to convey their letters to and from the post, and passes his newspapers along to them (thereby allowing them to keep up with the world at large while sparing them the expense of subscribing on their own).
The next day, the Dashwoods meet Lady Middleton, who is a fine young woman about 26 or 27 years old. She most likely married at about the age Elinor is now – 19 or 20 – since her eldest child (whom she brought along) is 6, and that age was entirely suitable for marriage for that time period. Lady Middleton is somewhat detached, and really only interested in her children. Her lack of conversation is probably not a real defect within her marriage, since Sir John is rather loquacious, but it doesn't make her a pleasant person to spend a lot of time with on her own.