How will I know for sure that the power supply I choose will have
enough of the right types of cables to properly supply electricity to
everything on my motherboard and case that needs it (cases nowadays
seem to have a lot of extras, like temperature readouts and bright blue
LED lights)?

Get a 550W+ PSU from good manufacturers like Seasonic or Zalman and you will
know that you don't have to think about all the issues you mentioned.