600 isn't a bad start, but its a little low for getting the best edge out of a chisel, especially one with good steel. You can find higher grits pretty easily. Check Walmart, they usually have the silicon carbide paper up to 2000 grit in the automotive section. 2000 is probably high enough, but what I like doing after I've hit that is take a piece of cardstock and charge it with green polishing compound, then use that in place of the sandpaper. Perfect mirror polish that way, makes for ridiculously sharp edged.
One last note, I hope you aren't using that 1x6 as the base for the sandpaper, as I can garuntee it isn't flat. With sharpening, you need a flat surface to get a straight edge on the blade. No flat surface means less than optimal results on the edge. And less than optimal is not good. I use a piece of granite countertop for my sharpening, but I realize that can be difficult to find. Glass plates are popular, but again, can be difficult to find. As far as something you can easily find at a local big box store, try and get a piece of either melamine or mdf. Both are nice and flat, and both are dimensionally stable so they won't warp. Both are also incredibly common
Before I forget, nice acquisition! Few things are quite as satisfying as taking a freshly sharpened chisel to some hardwood end grain and taking off paper thin shavings