Broccoli, cut up, put in bowl, place a plate that totally seals around bowl on top, nuke 4.5-6 min - try the shorter time first, it should be soft a bit, but not quite mush, add some olive oil or butter and a pinch or two of salt.
Other than the cabbage you have accent vegetables. While they have excellent properties, you will not likely eat the in enough quantities to get the micronutrients you want. For 7 oz. of broccoli cooked you would get a decent amount of vit A (betacarotene), vit E, half a days worth of folate (many people do not meet their daily need), and a days worth of vit C and K. Also about 20-25% of your fiber need.
As for meat, you could buy ground, cook it in a pan and then rinse with water. Studies have shown that it is mostly the fat that is removed and there is little loss of most nutrients. Chicken legs with skin are way cheaper and tastier, if you remove the skin after cooking, there is not that much fat left. Place it on a rack in a pan while you roast (75-85 min @ 350) and it won't sit in fat.
Spinach cooked in a pan on medium heat in a little butter or olive oil with a bit of salt, spices and herbs is also a nutrient powerhouse, I like to add red onion and 1/4 of any bell pepper that is not green.
If you are eating this clean, you will need to add salt to your cooking, otherwise your intake will be half of required. Usually 1-2g of salt spread over all meals and shakes.
Whole eggs are also an excellent cheap protein source loaded with nutrients. Due to the cheapness, you can afford to buy higher quality for the same price as cheap meat. These will have more micrnutrients than the cheapo eggs. I usually go for the omega3 ones, the chickens are fed flax and the eggs have a better fat mix (some would say ideal).
I would not worry so much about getting the absolute leanest cuts of meat, especially if your carb intake is lower, you will need some fat and most animal fat is not that bad. Supplementing with a couple tablespoons of flax and some cheap fish oil will nicely balance fat intake. By purchasing something like ground beef, you might be able to buy a higher quality for the same price, even once you work out the loss in weight due to rinsing fat.