Any of these grid spacings will divide evenly to those two dimensions (common factors of 1920 and 1080):
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
60 sounds the most useful to you, both vertical and horizontal grid lines go through the center point.
120 with 4 subdivisions isn’t too bad either.
Kalleheikki Kannisto
Senior Graphic Designer