How to start analysing and modelling data for an academic project, when not a statistician or data scientist
Typically, quantitative analysis is planned and performed, based on research study's goals. Focusing on research goals and corresponding research questions, researcher would propose a model (or several models) and a set of hypotheses, associated with the model(s). Model(s) and its/their elements' types usually dictate (suggest) quantitative approaches that would make sense in a particular situation. For example, if your model includes latent variables, you would have to use appropriate methods to perform data analysis (i.e., structural equation modeling). Otherwise, you can apply a variety of other methods, such as time series analysis or, as you mentioned, multiple regression and machine learning. For more details on research workflow with latent variables, also see section #3 in my relevant answer.

One last note: whatever methods you use, pay enough attention to the following two very important aspects - performing full-scale exploratory data analysis (EDA) (see my relevant answer) and trying to design and perform your analysis in the reproducible research fashion (see my relevant answer).