I need help with my garden removing weeds [included picture below] + ultimately replacing it with rocks?

Don't use Round up because that stays in the ground for awhile. I know its hard to pick them by hand, that works best though. You can use a pitch fork to turn the ground over and get the weeds that way and then pick them as the new ones grow. Once you get the weeds gone that you can, you'll never get them all, use mulch or a ground cover (weed mat) that will keep them down. The weed mat and mulch keep the weeds down but they help retain water and keep the ground warmer.