I think there is a slight correlation between a high level of physical fitness and acclimatization and that correlation is this, the better shape you are in, the less stress there will be on your body which will allow it to focus on acclimatizing rather than healing and recovering from the days activities. That having been said, most of the dozens of patients I have evacuated with serious altitude illness could be considered extremely fit at the time of their climb. Being in good shape has little to do with how well your body can and will adapt to altitude, but it doesn't hurt.
A lack of or restless sleep is more common that not at altitude, especially for your first night or two at a higher elevation. Our autonomic respiratory rates are programmed for our oxygen needs at whatever elevation your body is used to sleeping at. During the day, our need for oxygen increases and decreases based our activity level and we breath accordingly. While you may be shorter of breath than your are used to during a given activity, your body is still ramping up your RR to get the O2 you need during the day. At night it is different though as we go into auto-pilot. Your body wants to breathe as though you are still at sea level even though you may be at 10K. This results in periodic breathing also called sleep apnea and/or Cheyne-Stokes syndrome. Without getting too technical, your autonomic breathing isn't adequate and you wake up a lot. Diamox helps curb this significantly.
One major word of caution regarding sleep aids, many common sleep aids and drugs that include PM in the title include ingredients that are RESPIRATORY DEPRESSANTS! Taking sleep aids to combat the effects of altitude can actually compound the problem by suppressing your respiratory drive and further contributing to the source of the problem, a lack of O2 in your bloodstream. These sleep aids do the exact opposite of Diamox and what your body is trying to do, ramp up up your RR. I have seen this play out dozens of times. Folks with moderate AMS symptoms take a sleep aid to help them get rested and feel better and wake up with full blown AMS or edema. No bueno.
If you plan on taking a sleep aid at altitude, talk to your doc and make sure your drug of choice doesn't contain a respiratory depressant.
More bad news, alcohol is a very significant respiratory depressant.