Just trying to make sense of what you said, Jal_ut, and save needless confusion. You said ignore everything that's been written about companion planting, then gave advice on companion planting, like beans can help cukes by fixing nitrogen in the soil, or sunflowers can inhibit the growth of weeds. Sounds like companion planting to me, but should I and the original poster ignore what you just wrote?
I could have elaborated a bit more on this I guess. My point is that you can entirely ignore the companion planting thing and have a fantastic garden. Experiment with these things if you wish, but don't go into a tizzy about it until you have some experience. Right now it is nothing to worry about.
I see what you're saying about following corn w/sunflowers. Just sounded like he meant that you plant corn, then plant sunflowers so the two grow together and the sunflower keeps weeds from coming up around the corn, which also sounds like companion planting to me.
When I said follow sunflowers with corn, I meant sunflowers this year, corn next year. Not planted together the same year. You can google "sunflower allelopathy" for more reading on this subject if you thirst for information.
As has been said, feed the soil. This is the one most important thing we as gardeners can do. To that I like to add: "Give your plants space to do their thing."
The best fertilizer is the gardeners shadow.