Go light on the burdock root, it's kind of bitter. Dandelion root is decent, kind of like sassafras but not as pungent. Sassafras is going to give you the most flavor, but it being in a powder, it's a bit harder to work with.
I don't have it in front of me, but Stephen Cresswell's book Homemade Root Beer, Sod & Pop has a number of different root beer recipes. I don't know that there's one with exclusively those three roots, but browsing through there should give you an idea on how to adapt a recipe of your own.
If I was going to give a gallon recipe a shot with just those three roots, I'd probably steep 2 tbsp of sassafras powder, 1 tbsp dandelion root (assuming cut and sifted), and 1/2 tbsp burdock root in 1 gallon of water. (bring water to a boil, add roots, remove from heat, cover and let sit for a couple hours) Strain it twice, once using a muslin cloth then using a coffee filter to get all the sediment out. Add in 2 cups white sugar with 1tbsp molasses or 1 cup white sugar and 1 cup brown sugar. Then add 1-2 tbsp vanilla extract and a drop or two of anise extract. A pinch of citric acid wouldn't hurt either, but don't add more than just a pinch.
It's a rough draft, but that's where I'd start, anyway.