Software recommendation for creating videos for demoing research results
Just about any NLE could handle your needs.  Nothing in that listing seems particular difficult, though with a budget of $300 it might be easiest and fastest to pay an editor to put it together for you really quick.  Alternately, Final Cut Pro X could do it pretty easily since you are on the Mac platform and the most recent copy is just within your budget.

It is a professional NLE (non-linear editor) but there are a ton of tutorials available online to get you going quickly with all the basics and your particular needs are very simple to do.