Character Analysis
You could accuse Peachum of a lot of things, but he'd defend his honor and reputation to the death. He's a businessman, even if his business is shady; a family guy, even if he treats his daughter like a cash cow; and a law-abiding citizen, if you don't count the shady business. He's a model hypocrite, in Brechtian fashion.
An Entrepreneur
Peachum's shop is practically a charity—he helps the very poorest citizens of London find the equipment they need to beg properly and profitably. Okay, fine, we're being a little sarcastic here. It's more of an extortion shop, where beggars come to give almost all their money to Peachum to keep from being beaten up or worse.
But that's the tone that Peachum uses when he talks about himself. He's convinced that he's doing a great service: "Any man who intends to practice the craft of begging in any one of [the districts] needs a licence from Jonathan Jeremiah Peachum & Co. Why, anybody could come along—a pretty to his baser instincts" (1.1.85-88). Peachum sounds so official and legit that it's easy to ignore the fact that he's exploiting the beggars for his own profit.
Peachum, then, as a business owner, stands in for capitalist society in general, especially the bourgeois shopkeeper. Brecht is pointing out that everyone participates in society's thieving and inequality, but some of us are authorized to do so because we, like Peachum, disguise our thievery as business.
A Family Man
Peachum is also a fine example of the modern family man. Yes, we're being sarcastic, again. He talks the talk, but when it comes to actually caring about and for his family, he's a loser with a capital L. So, a Loser.
When Peachum finds out his daughter, Polly, is going to marry, he doesn't really care who the lucky guy is. He flat doesn't like it. We find out why pretty quickly, and it's not some kind of old-fashioned, fatherly chivalry:
PEACHUM. Wanting to marry her off? The idea! Do you think this lousy business of ours would survive a week if those ragamuffins our customers had nothing better than our legs to look at? [...] Marriage! I expect my daughter to be to me as bread to the hungry. He leafs in the Book. It even says so in the Bible somewhere. Anyway marriage is disgusting. I'll teach her to get married. (1.1.171-184)
Peachum is worried about money in the bank, not about his daughter's well-being and happiness. For him, family is there for his benefit, specifically his financial benefit, and nothing more. His vision of marriage as "disgusting" is ironic, too, by the way, given that he depends on his own marriage to make his business run.
A Law-Abiding Citizen
Besides being a respectable (ahem) business owner and a stand-up (guffaw) family man, Peachum is also a law-abiding citizen, respecting the rules of his homeland and doing his part to keep everything in line. Bahahaha. Okay, no, really, this guy is such a crook.
Peachum, in contrast to Mac, seems to be an upstanding citizen. He's always reporting crimes to the cops and spouting off about how the beggars need to follow rules to avoid chaos. But it turns out all his rule-following is just self-serving.
When Matthew, one of Mac's pals, congratulates Mac on seducing Polly Peachum, he says that Mr. Peachum will "tell you he's the poorest man in London" (1.2.21). It's that "tell you," which is so very different from the truth, that reveals Peachum's hypocrisy. While he pretends to be a humble, law-abiding citizen, he's actually a ruthless gang leader himself. The only difference is that his business and family are, at least on paper, legit, so the law is on his side.