Re: MOTO G Just purchased yesterday My first question...
It's a little puzzling to me that this would be a problem, since the long-press delay should be fairly substantial--a person would have to be keeping their finger on the screen for at least a half second before the request came up. Normal operation of any kind of Android device is short taps for selection, and long presses to bring up more options. If a person makes it a habit to keep a finger touching the screen, it won't work well. There's also the possibility that your device is faulty, and that it is detecting very minimal presses as a long-press.
That being said, you can try going to Settings>Accessibility, and look for a "Touch & hold delay" option. Set it to Long.