Your recipe appears to have enough acid and sugar to make using a "boiling water canner" sufficient. Once you have cooked your sauce and filled your jars (you are leaving a headspace aren't you?) and placing them into the water bath ... once the water begins to boil - then you start timing.
You didn't state where you live in your profile ... so it's impossible to give you a better guess than ... in boiling water somewhere between 20-35 minutes per pint. Altitude affects the boiling point of water ... the higher the altitude the lower the boiling point - and thus a longer processing time.
You might check out this page on BBQ Sauce
on the National Center for Home Food Preservation
website which has all kinds of food preseration information.