The subject isn't as difficult as it sounds initially, believe me.
Basically, every photo is taken with a particular shutter speed, a particular aperture, and a particular ISO setting. (And a particular White Balance too! You forgot about White Balance.) The key issue is how many of those things you decide yourself, and how many you let the camera decide.
You can take pictures in green box mode, and nobody will shoot you for it, and you will get some good ones. And of course it's safe for that 'quick' shot if you don't have any time to think. But sometimes you will find that the decisions that the camera made weren't necessarily the ones you'd have made. Maybe the shutter speed wasn't fast enough to "freeze" a moving subject. Maybe you'd have preferred the background to be more blurred. Maybe the colour cast is wrong. (Did I mention White Balance?) If that happens enough, and you care about it enough, then you will benefit from learning how the other modes work.
The think is, you don't have to do it all yourself. You can set the shutter speed to freeze the action, and the camera will do the rest. Or you can set the aperture to get the background out of focus, and the camera will do the rest. You decide what you care about, and what you don't.
So... learn about exposure - the best book, that everybody here recommends, is "Understanding Exposure" by Bryan Peterson - and you'll be able to take control over the camera and get those "great and inspiring photos" that you want. But you can always leave the camera in green box mode for when you want to take a quick snap.
And you can always ask people here for help and advice.