(a) don’t assume ordinary Joe can buy shares, at least during the IPO. The process (IANAA/B) is that a brokerage undertakes to sell the shares for a commission(!). They then sell subscriptions for the shares to valued customers and other quid pro quo arrangements (!) to all their friends.
(b) the theory is that the shares are priced at what the market can bear, but in fact these shares are often priced far below “fair market price” (or rather, “hype market price”) meaning the close personal friends of the broker get to pocket a substantial windfall by immediately flipping the shares for a signifcant profit. Basically, the underwriting broker steals from the company owners to pad their freinds’ pocket and gets a huge commission for their trouble and quite a few shares for themselves to sell.
© Joe Schmoe can now buy those shares once they are flipped at hype market price. If he holds them too long, the frenzy die down and he may actually lose money. That’s ok, it went to a good cause, the poor starving brokers of Wall St.
Going public generally allows a startup’s owners to cash in, (or cash out). There are limits to what you can do with shares if the company is ont publicly traded, but certainly you don’t get a feel for real value. What good is owning, say, Google or Pets.com if everyone says “wow, you could be a bilionaire” but you can’t easily sell any shares?
Theoretically the Joe Schmoes who own shares elect the board, but barring a huge social movement (I.e. “Let’s go green” or “dump the bum!”) generally board activity is a gentlemen’s game among the large collection of banks, mutual funds, pension funds, etc. that own most of the shares. Unless they seriously screw up, the company’s executive call the shots. A mutual fund, for example, can’t really push an agenda since their mandate is to maximize investor value. If they raise shit about a company they hold shares in, it better be in order to make the shares worth more. “Get out of South Africa/ Sudan / Burma”, “Free Tibet” or similar activist actions don’t usually meet this test.
OtOH, there were a number of reverse actions, especially in the 1980’s - take a public company private, assuming the market value of the shares is much lower than the company’s actual worth. (Read “Barbarians at the Gate”) A&P, Greyhound, or Woolworths, for example, used standard accounting rules to tally their property holdings. Often these were priced in 1920’s dollars for substantial downtown properties. Coupled with declining business, this meant that sellers of the stock may not realize that there was a lot of money to be made by breaking up the company.
The laws governing companies generally are much more restrictive for public companies - tranparency and governance rules, publishing public statements and verifying their accuracy. Besides having no restrictions on paying yourself as owner, private companies are much freer from government hassles.