Does minimizing hunger maximize weight gain?
Regarding the question in your title: minimizing hunger could be synonymous with leptin responsiveness. For example, leptin deficient or leptin resistant mice are known to become extremely obese - this is because leptin, the 'satiety' hormone, not only signals for you to stop eating, it also elevates the body's energy expenditure and stimulates thermogenesis. 

An interesting strategy I've heard, though I don't know how effective it is, is increasing leptin sensitivity through the composition of your diet. 

Another interesting element is that hunger, which is mediated by hormones such as ghrelin, decrease energy expenditure by multiple metabolic methods. So being hungry isn't always conducive to losing weight.

I believe most of the answer to your questions relies in these concepts. If you're talking about food distribution throughout your day, schedule it so that you're not very hungry for prolonged periods. Same with food type, eat foods that satiate for longer periods of time, unlike foods such as white rice. 

If you want to read up a bit more, I suggest looking into AMPK, and the role these hormones and food composition has on it. AMPK reading