GP wrote:

"... got a problem with my shoulder ligament, what kind of geometry is best then?"

I have a lot of physical issues and, by experimenting, I have found the fit that works for me.

The Bianchi Pista represents about the cheapest way to get into fixed gear riding, if a person wants a new bike.
I love my Pista, and it handles like no bike I've ever ridden or imagined.

I would suggest setting aside some extra money for a variety of stems, which will change the reach to the handlebars and their height.
My local bike store will change stems as many times as I want, for about the first month, free of charge.
It doesn't hurt to ask if they will work with you, and it cost a lot less than buying new stems, even cheap stems.

I have several very experienced, serious bike-riding friends who have made valuable suggestions.
Experimenting with moving the saddle forward and backwards, and up and down, and changing stems has made my bikes comfortable for me.

With my Pista, I simply flipped the Bianchi stem over, so that it rises a little instead of staying level.
I have put most of my energy into the saddle position.
It took me about a month to find the sweet spot for the saddle that makes my whole body happy.