Weed your garden first to eliminate the possibility of the weeds going to seed and germinating to compete with your new plantings for nutrients and garden space. Remove the remnants of spring and summer plants and pull up all the weeds and stray grasses. Prepare the soil as necessary and then set your new seeds in.
It is better to seed first. I would mow the lawn really short if you have a weed problem, then drop some fertilizer and sow seeds. Just make sure the area stays damp enough for the grass to take hold and get healthy.
Weeding to eliminate excess debris is important before seeding a garden. Remove the debris from the area. The soil needs to be able to harvest the new crops.
