Regarding the idea of a LW that provides width, why don't we leave the width to the fullbacks and sign an attacking leftback instead? Doing that would allow us to have a wide forward (Martial, Griezmann, etc) on one wing and a wide playmaker (Mkhitaryan, Mata, etc) on the other. Assuming we're playing 4-3-3, when the fullbacks burst up the pitch, our CDM (ie. Fabinho) would drop into the back line to form a trio. Personally, signing someone with the sole purpose of running down the line and crossing seems like a waste when we could easily leave that job to the LB. If we played 4-3-3, we could proceed like this:
WF (Martial/AG) ----ST----Mkhitaryan
--------------Pogba-------------Herrera
-------------------------CDM(Fabinho)-----------
LB---------CB----------Bailly---------Valencia
In attack, it would be more like this:
-----------------WF------ST
----------------------Mhiki
LB--------Pogba------Herrera-----Valencia
-------------CB----CDM---Bailly
I suppose Jose has his tried and tested methods, but considering our current personnel and our other targets, this makes the most sense imo.