Start with Fink, Primary Movement 1. This one alone will keep you busy for at least six months.
You are asking "why?" This exercise is at the heart of the Alexander Technique and schools that promote general proper posture. Depending on the bad habits that you have acquired over the years, this one will take a lot of time to fix.
Having said that, you can of course work on both books simultaneously and also go to later exercises in the Sandor book before having mastered the first one. Just be conscious about it.
I would also highly recommend Thomas Mark's book "What every pianist needs to know about the body". This book complements the other two extremely well. It also spells out directly what is wrong with many of the piano myths. With that, you have three books that will provide very good guidance. Now, all you need, ideally, is a teacher who knows about them, follows the principles presented, and who can help you work through them.
Finally, it is probably best to read through the books first without doing any of the exercises. This will give you an idea about what's in them, so that you can organize your further proceedings properly. It's like sight-reading through a piece first, before one starts working on it for real.
Topic: Should i start Sandor or Fink?