I don't know if there is any such thing as a perfect height. It all depends on weight/ build and geneology.
For my experience, I was 4'9" until I was 17, definitely the shortest kid in class. Then within a year or less (I don't even remember what it was like - it was that quick), I grew to 5'7". As you can imagine I was extatic and didn't really measure myself until years after. I must have grown very slowly after that because I don't remember my pants growing shorter, but definitely grew beyond age 21.
I am now 5'9", of course short by what is on this thread by I don't really have a problem with it. I think 5'9" - 5'10" is OK. Yes with dating girls too.
I am of the opinion, by experience, that its not the height by itself, it is also how you carry yourself, behave and act with a girl that "gets" you the girls. And let's not forget, average height of a woman is 5'5" - 5'6" so even at my height I would have no problems with 3" heels - ask women for their candid opinion and they will tell you that anything above this is really uncomfortable.
Something I think is true, didn't read any science books on this, but for guys (on average) you can assume that you will be at or above your fathers height. I think this is more true for heights below 6' than it is for above 6', where the variance is a little larger. But really is there a big difference between 6'3" and say 6' or 6'1"? In the grand scheme of things, there is more you have to think about than 2" in height difference, especially at or above 6'.