What happens when you pluck a guitar string?

[sophiecentaur]

How could the string be straight all the time. Do you actually have a proper picture in your mind of what a standing wave looks like over time?

 

[sophiecentaur]

How do the interference patterns give me the resonance? Are there waves on both ends at the same time and they need to be in sync? What would happen if the string isn't a multiple of half waves long, how would they interfere? Why do the overtones appear in the first place?

You are still having problems, aren't you?
You need to appreciate that this all takes time to establish. Enough time for waves of the highest frequency to have traveled back and forth and to have formed an interference pattern.
A stable interference pattern cannot be established for any waves but those allowed modes _ the overtones and fundamental.
When you get down to it, you have a system that can only vibrate at certain frequencies so it can't oscillate any other way if it is left to itself.
Imagine a mass on a spring. There is only one frequency for it to vibrate at once you let it go. Now try adding another mass, hanging on the bottom on another spring. More complex but you could still only get vibrations at a limited set of natural frequencies. The masses will go up and down and together and apart. You could choose any setup to start with and you'd only get those normal modes of vibration. (Violent disturbance so they collide is not allowed, of course) I don't think you could argue with it so far.
A taught string is just another system that can oscillate in certain modes. Once it's been let go it cannot vibrate in any other way but in a combination of these modes. Before you try to argue against the why's and wherefores of traveling waves, nodes and standing waves you just HAVE TO accept the above.
This means there can only be certain waves on the string. These have to have lengths which actually fit into the space between the ends of the string.

I think it's time for you to do more thinking, reading round and not to keep coming back more questions. You need to cut the apron strings.
:-)