Mulch well. A decently thick layer of some sort of organic mulch will keep weeds to a minimum, allow those that do appear to be removed easier and will help to improve soil conditions.

Hmmmm… Interesting! Now I’m wondering whether I might be getting some of those…! I did some searching for info - they are native weeds that are common and invasive as the annual seed production is high and, as the seeds are very small, the seeds are spread by the wind. A lot of the plants are resistant to common chemical weed control. Much of the info on-line is aimed at commercial crop producers as horse weed has become a big problem in no-till production. As gardengal suggested, mulching can help in gardens as burying the seeds can reduce germination and very competitive companions can also help. This article from Cornell had lots of good information on it.