There are many different ways to make your own BBQ sauce, but most start with a tomato base of some type, then add the seasonings and flavorings you like. Some like to add honey, others brown sugar or molasses. I've never made hot sauce, as I don't particularly care for it.
For hotsauce, all you should need is hot peppers, vinegar and a little salt. BBQ sauce is one thing to make but do check the ingredients on the hot sauce bottles in the grocery store. They usually don't contain anything that isn't natural and it would be far more convenient to buy hot sauce than to make it. In the summertime, we just go pull a jalepeno or two from the garden and leave the hot sauce in the cabinet. It's all good.
For BBQ Sauce it will vary.
East Carolina uses vinegar for a base.
Kansas City uses tomato or ketchup base.
Memphis uses more vinegar and molasses then Kansas City.
South Carolina is more of a mustard base.
Texas tends to be a thinner sauce using cumin, chili peppers, bell peppers, chili powder, onion, lots of black pepper and a small amount of tomato.
Alabama has a mayo based sauce.
Other countries use things like Hoisin sauce, yogurt or soy sauce.
Mine would be a light tomato base, since I am not that fond of it but spices is where it would be for me. We all have a difference of opinion considering how mild a sauce should be, I bet we would be making a few different ones in our household.