How we cite our quotes: Section.Part (if applicable).Paragraph
Quote #7
I esteem the man whose self-love, by whatever means, is so directed as to give him a concern for others, and render him serviceable to society: as I hate or despise him, who has no regard to any thing beyond his own gratifications and enjoyments. In vain would you suggest that these characters, though seemingly opposite, are at bottom the same. (AII.4)
Selfishness often gets a bad rap but is it always bad? People use "selfish" as an insult but we all have different sides to our character. It's not as though a person must either be totally selfish or have zero regard for their own life and happiness. That's what Hume is getting at here, stressing that we can care about ourselves and others. To slam self-interest as a whole is lazy and way off-base (just ask Ayn Rand).
Quote #8
Nature must, by the internal frame and constitution of the mind, give an original propensity to fame, ere we can reap any pleasure from that acquisition, or pursue it from motives of self-love, and desire of happiness. If I have no vanity, I take no delight in praise: if I be void of ambition, power gives me no enjoyment: if I be not angry, the punishment of an adversary is totally indifferent to me. (AII.12)
Building on his comments about self-interest, Hume again argues that it's in our nature to have a degree of ambition, vanity, and desire for recognition. These things shouldn't automatically be classed as vices, as they give us a sense of motivation. They will us on to succeed when we'd otherwise just shrug our shoulders and say "whatever."
Quote #9
Good-nature and honesty, especially the latter, are so indispensably required, that, though the greatest censure attends any violation of these duties, no eminent praise follows such common instances of them, as seem essential to the support of human society. (AIV.4)
There are some virtues that are rare and inspire a lot of admiration—acts of heroism, grand gestures of kindness, or sending your best friend silly cat videos, for instance. However, virtues are often just a part of day-to-day life. Hume sees honesty and a pleasant character as being expected of us all, with failure in these areas opening us up to criticism. Some folks may be lacking when it comes to these qualities, but they're seen as so essential that possessing them is no big whoop.