I don't generally cook for the whole week, but will cook for a few days at a time. I generally cook a few pounds of ground beef (just in a pan over medium heat). When I drain the liquid and fat from it, I use the liquid for cooking rice. If you mix the beef and rice, then you can easily add bbq sauce, or beans, or pasta sauce. For vegetables, I focus on stuff that can be eaten raw and just cut it up (orange bell pepper, salads, etc), or the microwave in bag frozen vegetables.
Another very good option is using a large slowcooker. You just put potatoes, meat, and vegetable in, leave it overnight, and then you have food for days. It is easy to get simple recipes for a slowcooker, and they often use cheap and nutritious ingredients.
On Youtube, the video "Meal Preppin' with Alan Thrall" gives a pretty simple setup for prepping a lot of food at once.