Yeah just install it on the PC and set it up and try it out, given your specs posted in your original post it should be fine though.
Launchbox is the desktop "management" mode though many people such as myself actually use it in this mode 99% of the time anyways. BigBox is the "cabinet / htpc" mode where its controlled using a joystick or controller. This is the mode and exe you will use in your cabinet and it's a part of the same download, no separate download at all.
Ignore the Launchbox.Next.exe file, that is a part of the current beta and will be replacing the standard Launchbox.exe in the future when it's ready.