Yes, a student license will be adequate for these purposes. The basic purchase of a student license comes bundled with the following toolboxes.
Simulink, Control System Toolbox, Curve Fitting Toolbox, DSP System Toolbox,
Image Processing Toolbox, Instrument Control Toolbox, Optimization Toolbox,
Parallel Computing Toolbox, Signal Processing Toolbox,
Statistics and Machine Learning Toolbox, Symbolic Math Toolbox
These alone will be sufficient for most of your works. But If you want to get another toolbox, you can get it for a small price.
Since at the time of the purchase of a new student license, you can get additional toolboxes at a lower price; therefore, I suggest you look at Simscape and Simscape Multibody toolboxes. These will be very useful for Rigid-body dynamics analysis in Simulink.
