Most of our ground was outdoor pig lots for many years. The people sold out of hogs, tore everything out and cleaned it up. Then several years later another person bought the ground and moved a house here. We bought several people later. Point is, we have more weed seeds than I know what to do with. One way we deal with weeds has been plastic mulch. Another way is by using scuffle hoes.
http://www.prohoe.com/scuffle_hoes.html
These hoes really make short work of weeds. If you are willing to put in the time, you can weed several hundred feet of rows in about 15 minutes. When ever I check garden, I always carry one with me and weed as I go. They work like a mop and just slide on top of the soil.
Another way we deal with weeds in to try not to water them by only using drip tape. Last years drought, we hardly had to weed between the rows.
Final way we combat weeds is we transplant almost everything. This way the plants can have a head start choking out the weeds by reducing sunlight.
We have also used straw mulch, but I am never 100% happy with it. Sometime I feel it brings in more weeds than it prevents.
Jay