The regular and best families Emma could hardly suppose they would presume to invite -- neither Donwell, nor Hartfield, nor Randalls. (Chapter 25)

I read it as the regular and best families were the same families—those at Donwell, Hartfield and Randalls. The word regular describing families Emma is in the habit of associating with. LOL! However in Chapter 19 Emma mentions two levels of society in Highbury, both of which she is not a part of leaving a third for her sphere of people.

She had had many a hint from Mr. Knightley and some from her own heart, as to her deficiency -- but none were equal to counteract the persuasion of its being very disagreeable, -- a waste of time -- tiresome women -- and all the horror of being in danger of falling in with the second rate and third rate of Highbury, who were calling on them for ever, and therefore she seldom went near them. But now she made the sudden resolution of not passing their door without going in -- observing, as she proposed it to Harriet, that, as well as she could calculate, they were just now quite safe from any letter from Jane Fairfax. (Chapter 19)

I think the Best society according to Emma is Donwell, Hartfield, and Randalls. However I don’t really know who to put in the second rate and third rate of Highbury—for example where do the Bates go? Could the second rate be described as regular—it sounds a bit odd and luckily I am now out of speculations on this subject.

They had been speaking of it as they walked about Highbury the day before, and Frank Churchill had most earnestly lamented her absence. Might not the evening end in a dance? had been a question of his. The bare possibility of it acted as a further irritation on her spirits; and her being left in solitary grandeur, even supposing the omission to be intended as a compliment, was but poor comfort.

It was the arrival of this very invitation while the Westons were at Hartfield, which made their presence so acceptable; for though her first remark, on reading it, was that "of course it must be declined," she so very soon proceeded to ask them what they advised her to do, that their advice for her going was most prompt and successful. (Chapter 25)