Mac OS X cannot start up from this disk

good evening! I am having trouble reinstalling OS X loin on my MacBook Air late 2010 version. I followed the directions of several you tube videos on how to erase and reinstall your OS on your Mac. First I held down the option key and power and chose the disk utilities and then I clicked on machinist HD and clicked erase ( I think this is where I messed up) and then I closed out and attempted to install Loin. I accepted terms and conditions and then I chose Macintosh HD drive to install and then once provided my user name and password, it told me that it was not available and to try again another time.

BAckup plan plan was to use my installer drive that came with my computer that has the OS on it. I have attempted to get it installed and I keep getting to the screen that says Mac OS and select a disk where you want to install Mac OS X and it has the yellow triangle with the exclamation mark on it saying "at least 59.65 GB free 59.81 GB total." I am assuming I have enough room to install. And why I choose this one ( which is the only option I see) it says " Mac OS X cannot startup from this disk"

i know I am doing something really wrong..probable many but how do I just reinstall it? Have I ruined my Mac?

i have included some snapshots of my troubles