I would personally not use PT because that indicates Physical Therapist.
With regard to using something different than a dot com–although that may be the most common that we look to–there are so many new extensions coming out that eventually it just comes down to what you want.
Hope this helps and good luck.
Aside from the possible confusion with physical therapists (so therefore, .cpt might be better), I think that having a more common ending like .com makes it easier for trainers to get ‘ancillary traffic’ when people are casually browsing the internet, which might not be the case with .pt.
While the .com’s are becoming more scarce you will no doubt find more and more other extensions. Aside from the .com more common and easily remembered extensions are .net, and .us. However if you can get a .com you’re better with that one. The .org is generally reserved for non-profit organizations, charities etc.