Why are some potatoes better than other for frying or making French fries? What is the chemistry in that? And how do I apply this method in selecting different veggies for different uses?
It's all about starch content of the potato. Waxier potatoes are wetter, meaning they have a lower start content and higher water content. They don't fry that well because they have too much water to crisp up properly. Starchier, drier potatoes are better for thin fries, but they aren't as good for chunky fries as they are actually too dry to give a fluffy inside. For chunky fries (aka chips), wedges or roast potatoes you want a potato with a medium starch content.
As for application to vegetable selection nothing comes immediately to mind, potatoes are vegetables from a botanical point of view but from a cooking point of view they are very different from most other things you prepare. Potatoes are just big balls of starch and water, so the advice above would only apply to foods that are structurally similar, like sweet potatoes and yams.