Is it safe to reformat drive during Recovery Mode install?
The difference between the 500gb and Mac HD is pretty simple actually. The parent is the actual hard drive that holds the partition (Mac HD). You use that to re-partition if you want to split or change the partition table.

So you should use the Mac HD if you just want to erase and install.

The disk1 in your screenshot is the recovery partition. You probably can't erase it or remove it (not sure as I haven't tried). The icon indicates that it is a mounted drive and not an actual hard drive.

So click the Macintosh HD, erase, format, target for install. It's not long ago I did the same on my MacBook Pro.

Happy fresh laptop!