You can download a parade tracker app on your phone. It will help you see the parades and what time they all roll.
Saturday night is the popular Endymion parade which runs through Mid-City and then downtown. There is no Saturday night parades going down St. Charles. Depending on your reservation, you could get into the Quarter Saturday night, but heading there early evening to get across the parade route is your best bet.
Also, keep in mind these parades have to set up, so depending on where you the parades can affect you even before they begin.
Sunday is pretty much parades all day and night non-stop. Bacchus is a huge parade that night and it gets super crowded.