TV's in general are very poor for gaming provided your using a desk, way too large for how close your sitting to the screen (which exacerbates its low PPI) and they have much worse input lag than monitors.
And as mentioned, 120hz TV's are interpolated, meaning its not receiving true 120hz input and displaying but, but examining two sequential frames and adding in what it thinks goes between. Again, more input lag for this calculation.
If your gaming on a coach, then you kind of just have to go with a TV. A 24" monitor from two meters away is a bit too small, even with such awesome colours and minimal input lag
If your dad is really set on 120hz, get a 120hz monitor. Though your PC will need to be fairly beefy to make it worthwhile.