Just to clarify Walter's 2nd comment, he's suggesting a compute cluster. What you're saying is that your university does not have an HPC cluster/data center, correct? If it does, that could be an easier approach.
To use MathWorks Cloud Center, someone will need to start a cluster using an AWS account, which needs to be paid for by someone (you, the university, etc.). The MATLAB Parallel Server license may already be available for you. Best to contact Technical Support (firstname.lastname@example.org) to find out what you are entitled to run and where.
Regarding the best EC2 instance, without knowing anything about your code (how long it takes to run, memory required, CPU/GPU, etc.), it's impossible to make a proper recommendation. My suggestion would be to initially start small, get accustomed to running jobs on AWS and then scale over time once you get the hang of things (again, someone will need to pay for the compute time even if the licenses are already available). Overtime, you'll want to familiarize yourself with the different supported instances, but I would suggest the m5.xlarge to begin with. It's got 2 cores, which helps compare it to the results you got from your Mac. If all goes well, then increase the core count to an appropriate number (i.e. you might get diminishing results with a 32 or 48 core machine).