I have to say that I had never owned a male dog before I got my great dane. I really didn't have a preference for male vs. female, but my husband had all of your concerns and also the whole red excitable penis freaked him out.
In the six years that he graced this planet, and he was neutered at about five or six months (can't remember), I can honestly say that I never saw any excitable penis nor did he ever mark inside my house or anyone else's house. He was a very loving dog who bonded in a way I had never bonded with my female dogs, I would have to say that it wasn't more of a bond, but it was a different bond and I'm happy I was given that experience.
With Posh, I have had the embarrassment that goes along with a "dominant bitch" as my agility trainer lovingly described her. I've read in a couple of sources that havanese are a matriarchal breed and that many times the females do just as much mounting and marking as the boys. I have experienced Posh marking her territory in the tunnels at the agility class, not cool, and at my in-laws house to show the totally passive cavalier who was boss. I have also stopped Posh from her "humping escapades" as she tried to hump every dog that came over to our house.
Meanwhile, I don't know how a dog could be more loving than my Posh girl is. Honestly, I didn't care what sex of dog I got, I just knew she was the right one for me the moment I set eyes on her. I could feel it in my heart, and at that time she was the breeder's show puppy so I had to dismiss the idea. Obviously, everything worked out.
My final advice, open your heart and your mind and the right dog will find you. (I'm assuming that this right dog will come from a responsible ethical breeder who is working diligently with health tested dogs to better the breed
!...or will be a rescue