This question has many possible answers. At different times in history, circumstances were different. And so the answer, depending on where you look could vary. But it seems most appropriate to offer the kabbalistic answer most appropriate for this time.
This can be found from the Ba'al Shem Tov as written in Keter Shem Tov, page 3:3. It is preferred that one immerse as frequently as possible and in particular in times of need.
On page 125, chapter 219, the Ba'al Shem Tov attributes all the revelations and levels to which he attained being the result of immersion in the mikvah constantly. He emphasizes that frequent immersion (יותר בתמידות) is more beneficial than frequent fasting. He says this is because fasting weakens the physical body from being able to serve HaShem. He says that it is better to take the strength that one would lose through fasting and direct it toward increased Torah study and prayer with proper kavannah with all ones might.
Additionally, on page 409, chapter 254, he emphasizes that in particular it is beneficial to immerse on erev Shabbat and Yom Tov and also on Shabbat and Yom Tov morning because it gives one 'hope' (a play on words for 'mikvah'). He says immersion at those times is a segulah for praying with kavannah and for cleaving with G-d.
In regard to the different 'spiritual effects' relating to the different times of day, these are according to some sources, like Sefer Raziel HaMalach, divided into four categories. Each of these four time periods corresponds to the predominant influence of the corresponding names of 72, 63, 45 and 52 as well as 161, 161, 143 and 151. A discussion that may answer some of your questions concerning this can be found at the section of Keter Shem Tov explaining the Kavannot for immersing in the mikvah according to the Ba'al Shem Tov. A link follows.
Concerning the subject of men and women, the general custom today is that women who have not yet been married do not immerse. But the reasoning behind that has nothing to do with concept here. Strictly speaking, both men and women benefit from this practice in the same way. There are some women today who immerse more frequently than once a month.