If you are going to use a weed killer spray, you need the plant leaves to stay on the plant so they can absorb the spray. So don't weed wack.

But since you don't need to use the garden until next year, you could forget the spray and just cut down the weeds. Then you could lay newspaper (about 3 sheets thick) over the area and then put leaves or other organic material on top to hold the paper down.

Which "weeds" are in that planting bed?
Will the "weed" killer you plan to use kill those "weeds"?
As Kimba has already proposed laying something impervious, such as newspaper or cardboard, that will deprive those "weeds" of access to the sunlight they need to live and grow will kill them with very little harm to your environment like a "weed" killer can. Covering those "weeds" like that might also eliminate the need to turn that soil, cutting your work about in half.

Three sheets of newpaper is just fertilizer. Please use a much thicker layer for smothering live weeds or grass, or it may not work.

This question is asked often. You might find some of the info in this discussion or this one helpful. Killing weeds/grass doesn't need to involve actual work or chemicals. How much fun will I have with this new spot next year? A lot!