I think that first comes the choice of the film. In color, you should use low saturation films, which are those intended for portraits, and are usually coming in low ISO (50, 100, 125). In B&W, I would recommend the T-grain films, no matter their speed.
Second, comes the contrast of the light. You mentioned the early mornings, I’ll add the days with covered sky, and the hours most photographers avoid to shot: around the noon (because at this time the light might be lower in contrast – so, you should shot at noon). By late morning and evening, the light tends to achieve a higher contrast. Look for shadows: if you don't see much, the light contrast is low.
Third, in B&W, development controls the contrast. So, if you want to lower it, overexpose 1 stop and underdevelop 20~25%. And if you want an even lower contrast, overexpose 2 stops and underdevelop 40~50%. This doesn't work in color (or at least, this is what I know, but I never developed color negatives myself).