I'm not an expert on organics and GMOs and pesticides but I do know a few things.
First of all, people think of pesticides as this foreign thing that only exist when humans introduce it to the environment. But that's not the case. Forget humans for a minute. Plants exist and bugs want to eat them. As a result, plants evolve pesticides as a defense against bugs. IOW, pesticides are an integral part of the plant. We don't think of them as pesticides because they're not added by humans, but a pesticide is just something that harms a pest. In each generation of plants, the ones with better defenses against bugs have a better chance of surviving and passing on its genes. Plants are completely indifferent to whether humans eating the plant for a few decades increases the humans chance of getting cancer.
I think part of the misconception about this stems from the idea believed by some that nature is somehow perfect to begin with. Nature is what it is and it's something to hold in awe and that's fun to learn about, but it's not designed to maximize our well being.
In fact, most of the "natural" plants we eat aren't really natural in the sense that they would not grow without human intervention. They only exist in the first place because humans crossbred earlier versions of the plants, which is a primitive form of genetic engineering. And they only continue to exist because humans cultivate them. They are both better for us and less natural then their earlier versions. Google "natural banana photo" and see if you want to eat it. Those beautiful big yellow bananas you get in the grocery store BTW are clones and wouldn't exist without human intervention.
As far as organic food and pesticides goes, it's not the case that organic food doesn't use pesticides but rather they don't use synthetic pesticides. Scientists create synthetic pesticides and figure out what they do and they have to test them before they can use them, yadda, yadda, and those are the ones used in conventional agriculture. In organic agriculture you can still use pesticides but they just have to be naturally occurring pesticides. Of course, just because a pesticide is naturally occurring doesn't mean it's any better (or any worse) to consume than a synthetic pesticide. The "natural" or "synthetic" aspect doesn't enter into it, rather all that matters is what happens to your body when you ingest it.
As far as GMO goes, that's just a technique of moving a gene from here to there. You move a lot of genes all at once if you crossbreed plants. Moving genes is just a tool and isn't inherently good or bad. Because it's a tool though, it CAN be used for good. Nature isn't perfect and human-created tools can be used to improve on it. How you use the tools is what matters.
People get crazy about food. I live in a area that has a lot of foodeis and it isn't an exaggeration to say that it equates to a religion with some people. To keep things straight it helps to follow what the science says. There's a lot of crazy rhetoric out there on the Interwebs. When you're reading something always look at what the source is and evaluate it's trustworthiness.