The paper describes BIRAFFE2 data set, which is a result of an affective computing experiment conducted between 2019 and 2020, that aimed to develop computer models for classification and recognition of emotion. Such work is important to develop new methods of natural Human-AI interaction. As we believe that models of emotion should be personalized by design, we present an unified paradigm allowing to capture emotional responses of different persons, taking individual personality differences into account. We combine classical psychological paradigms of emotional response collection with the newer approach, based on the observation of the computer game player. By capturing ones psycho-physiological reactions (ECG, EDA signal recording), mimic expressions (facial emotion recognition), subjective valence-arousal balance ratings (widget ratings) and gameplay progression (accelerometer and screencast recording), we provide a framework that can be easily used and developed for the purpose of the machine learning methods.