Another tip I forgot to mention. My 3-jaw chuck I use is fairly new to me, bought it almost 20 years ago. The back plate I have for it is made from a piece of 4145HT found in the old family machine shop dad had. At the time, no cast iron to be had. Works just fine. When I go to mount it to the threaded spindle, I'll coat the threads with never-sleigh to prevent galling. Anyways, the register on the back plate is turned about .010" undersize to the chuck counter bore. I do this to get the chuck running true to the material I chuck up on. Leave the mounting screws snug and bump around the chuck until you get as near as you can to zero runout. Tighten the mounting screws. They don't have to be gorilla tight, but Allen wrench tight. The chuck is not going anywhere. In the twenty years, I have not had an issue with the chuck moving around. Have had to re-adjust a time or two over the years. Remember, this is on a 9" SBL. Your mileage may vary.
Having a chuck that is running dead true does help a bunch on machining a cross feed screw to run true end to end.
Ken