This might sound odd, but the type of Yoga actually doesn't matter.  Iyengar, Ashtanga, Hatha, etc etc.   I personally do Ashtanga.  It is more flow based.  Throw in some Hatha to push for balance and strength.
 
But none of that matters.  The mistake I've come to learn about Yoga is that it actually isn't about the physical practice.  The real aim is to just be present no matter how poorly you actually do the various poses.  And is as hard as you might imagine, but is also the entire point of Yoga.
 
As a personal preference, check out on YouTube "John Scott The Wheel of Ashtanga Yoga"
 
I found his video magical in terms of explaining Yoga holistically. 
 
@`Erik Cason `believe that you would really enjoy that video too.  Not only might it be what you are looking for, but I do believe you would find alignment with John Scott.
 
Keep in mind, all of this is just one person's humble opinion. 
 
That said, I can attest that Yoga has been transformative to many aspects of my life. 

 Thanks for your detailed response. My wife did Iyengar before. But I always thought they did physical exercises which used a lot Auxiliary tools, chairs,  bricks etc.   

 If you've not done yoga before, just find a "beginners" or "basic" class and start from there. 

No need in those classes for anything except for maybe blocks if you need assistance in the beginning when doing the poses.