Can someone recommend me which whay to take, will these simple formulas save the day or do i need to dive in the textbooks? Thanks!
You are over thinking this. First of all, if you approximate the continuous form of a PID algorithm in the discrete time domain (all real industrial controllers do this), then the tuning will work out fine as long as the sampling interval is short enough (e.g. at least 10x faster than the dominant time constant of your system).
Secondly, if you use the manual tuning method or Ziegler-Nichols method (see Wikipedia article), then you do the tuning with the actual controller online, so the sample interval is automatically taken into account. In the real world people tend to tune the controller less aggressively than theory indicates, so don't worry too much about stability. Just de-tune it a bit if you see too much overshoot or oscillation.
Tuning controllers is an art, not a science. If you try to apply too much science you will just make things too complicated.