My preferred method for starting a new bed is to kill the grass with glyphosate (Roundup). I then till up the area, working in the old sod, which adds a great deal of organic matter. If you're patient, you can also kill the sod by covering it with black plastic. If you prefer you can strip the sod away by cutting it out with a shovel or sod cutter. If you have use for the sod elsewhere in your yard, this might be a good option since you plan to bring in extra soil anyway. Otherwise, it's a lot of extra work which is unecessary.