I am truly impressed when people come asking the right questions. Very nice!
If I want to buy crypto, then I believe I have to go to a broker or an exchange (assuming I don't know someone who wants to sell me some). So I've got to pay them. Are they regulated enough that I can be confident that they won't just run off with my money once I've paid them? Can I pay be credit card? Then, once I have bought from the broker or exchange, do they transfer the crypto to a wallet that I control? Or do they keep the crypto in their own wallet as a custodian? If so, again, how can I trust them?
You have to keep your eyes open, since the space is full of scammers, some even claiming to be good businesses (or even impersonating such businesses).
So you have to do a proper research on where you buy your coins from and pick a business/method that has already passed the test of time.
And indeed, you have to make sure you withdraw the coins to your own custody, just this means yet another learning curve, since it has plenty of security implications.
If you don't have computer management/install skills or the amount of cash you want to spend on buying coins is 4 digits or more I recommend you just do a quick research and buy a hardware wallet, they're the easiest path for "safe enough" self-custody.
It worth mentioning here that some exchanges may offer you (cheaper) bitcoin withdrawals on other chains (usually BSC or ETH). Beware, those are not bitcoins, those are altcoins ("wrapped" bitcoins) and I would stay away of those.
Also, is there an advantage to buying from a broker over buying on an exchange?
Some ask for KYC and not everybody wants to give that out.
Then the known exchanges have quite some not-so-small withdrawal fees (they falsely call them transaction or network fees, but it's more than that), hence if somebody buys small amounts sometimes the brokers come out cheaper (although the price is bad/expensive, if we consider/add the withdrawal fee too then it may come out cheaper).