I think it's worth pointing out that there are two extremes to the "counter" strategy. Hopefully, this will help people get to grips a little more with how TIs create a playing style.
In the popular press at the moment, there is a debate about the relative strengths and weaknesses of tika-taka versus the direct, counter-attacking of the Madrids and pre-Pep Bayern. In FM terms, I would regard both styles as being Counter strategies, but with a very different set of TIs. I'd actually regard the lower end strategies as being the "go-to" strategies for those trying to recreate the modern styles of play adopted by elite teams, especially those that play with many players the deeper strata. Cleon's thread on defensive systems and Ackter's on developing a modern catenaccio are fascinating takes on this idea.
Barca play possession football with a high-pressing system, as detailed in my OP. In FM14, that would mean Shorter Passing, Retain Possession, Play Out of Defence, Much Higher Defensive Line and Hassle Opposition, but with a Counter Strategy for the reasons I gave in the OP. The Madrids play far more direct football with a low-blocking system. That would mean Direct Passing, Higher Tempo and a Lower Defensive Line, but still with a Counter Strategy. Once you have this sorted out, they key is getting individual players to perform as you'd wish via Formation, Roles, Duties and PIs. These will heavily influence team shape and what the player does on the ball.