I had a vegetable garden overrun with witch grass once. I didn't know what it was at the time and used a rototiller on it. Big mistake. Made it much worse. It got to the point that I gave up on the garden for two years. Then after research, I decided to use a large piece of clear plastic leftover from an ice rink we had n the yard, and covered the entire area that was about 25x25 feet, with the plastic, weighed it down with bricks and left it there for a whole year. It worked great. We were able to reclaim that area and I got rid of about 90% of the witch grass. I don't know anything about bermuda grass, but I'd research ways of getting rid of that. I can't see using a chemical to get rid of it, in a 50x60ft area where you are going to grow food. If you can't do that, I would think thick cardboard with heavy mulch would be your next best bet. And it will improve the soil and increase your earthworms.

Read what Kimmsr wrote again. It's right on the mark. "The best mulch material to use is that which you can get at the least cost..." Check things out around you. It's amazing sometimes what you will see and find and get if you ask. All my leaves get blown away in the fall, but a mile down the road my neighbours will gladly give me their leaves. One neighbour has a nice stand of pine trees. He used to rake underneath them and throw out all the needles until I asked him for them. All I do is supply the garbage bags for them and go get the bags. My neighbours on the opposite side of the road use to complain about the seaweed washing up on their beaches but now they don't since I go get it for mulching particular beds and for my compost. I collect used coffee grounds on the way home every day. The owner of the establishment where I get them from cut his organic pick-up fee by 1/2 and is most pleased to see me. The following is mulch which I created with used coffee grounds (UCGs), pine needles, and shredded leaves. The following is a photo of the gardens where it was applied. I never had to weed this area the whole season. :O) Mind you, I weeded before placing the mulch and I don't do the newpaper things to snuff any weed seeds, but placing a good 3 inches of this mulch works well. If the plants were further apart or I was not introducing new plants to the gardens all the time, then I might be inclined to put newspaper down. I must agree with those who speak negatively of landscape/weed fabric. One experience in my parents' gardens showed me that it can be more of a pain than anything else. It provides no food value to the soil and will permit rhizomaceous weeds to creep underneath until they see a way out and by that time your problem is more than you'd like.

I agree with mulching. I worry about extending my garden beds due to the wild violets. We managed to pull the bulk out of the front bed, but it took an entire summer. My in-laws were visiting and bored during the day so would go out and dig down to the roots. They are persistent buggers! I have followed up this year by putting a second layer of thick mulch and taking any foliage off in order to starve the roots. Beside the stray leaf and weeding a lot before the mulch was put down, I have barely needed to weed. Whatever does grow through is weakened by having to push through the mulch. My lawn is almost 100% weeds dispite reseeding every Spring and Fall. I am planning on reseeding the lawn soon for the fall and then placing the feed pellets as an organic preemergent in the Spring. Might help with the garden, too if the lawn stops being one huge weed.... :)

I do not have any special advice for you based on which grassy weed that is. Generally, the options are mechanical removal (machines, hand pulling, hoeing), chemical (weedkillers, pre-emergents), or burning. Each has risks, sometimes substantial, and different effects. At the very least I do not see rhizomes in your pictures which might indicate you have a chance at getting ahead of these things. What do you want to have there eventually? Nature will fill any bare soil with plants in a very short period of time, even if you kill these. If you don't want this grass, plant something else to crowd it out. Find out what is native to your area and will crowd out the grass roots. If you want bare soil for a few months while you build, cover it with black fabric or plastic to prevent anything from growing.