Which fit model should I choose to analyze my signals?

Ideally, one should start with a scientific hypothesis for the model (e.g. “I expect a basic one-to-one binding process.”). This hypothesis is then tested against the data.
If you have no (good) idea about the process, start with the simplest / most confined model and gradually increase model complexity (number of free parameters) until the model shows acceptable agreement with the data. From a mathematical viewpoint, “acceptable agreement” is defined by goodness of fit statistics, e.g. Χ²-based p-value for nonlinear least squares fitting. Keep in mind that the more complex the model the harder to interpret its parameters.
For kinetics signals, for instance, we recommend starting with a complete-dissociation model that forces the signals back to baseline (at infinity). Only allow for remaining offsets (incomplete dissociation) when the strict model fails.