I believe the default shell for at least the last few releases is bash, so you'll get straight to it (though I have mine set to tcsh). If not, just type /bin/bash to start a bash shell.
Random password generator sites are fine - all they do is generate a random sequence of characters. However, you're probably going to have to write that password down to remember it, which makes it less secure. Better to come up with a sequence that has some mnemonic meaning to you, that contains uppercase and lowercase letters, numbers and other characters, and is at least eight characters long.
I doubt there's any need for the "general Mac user" to be using a shell, but if you are interested in programming or getting to know how the OS works "under the hood", then it's worth learning about. There are any number of good resources on the web about UNIX shells.