Its not registered users that is dependent upon the performance, but users online and interacting with Moodle.
You can have a million users registered on a moodle running on a Intel Atom based CPU with 1GB RAM, so you dont have to mention the total number of users, but concurrent is the figure that you have to keep in mind which you said 300 and taking quizzes, where quizzes being 2nd most power hungry task in moodle (chat being first), ideally you have to have database on a separate drive and on SSD (if you can't afford to get a separate database server) as throughput is tremendous during Quiz sessions, 1000's of Read/ Write operations per second so you can imagine the load.
Where you mentioned 8 core, in what specs? as a 4-core Hyper Threaded CPU will show 8 cores as well, but 4 are physical and 4 are virtual making it total of 8 logical cores.
Though you haven't mentioned RAM, but as per Moodle recommendation and you must have read it already, its 10-20 users per GB, now the upper figure of 20 for those who are online and not interacting hard with LMS and lower figure of 10 for those who are taking quizzes, so if your all 300 users will be taking quizzes at the same time, then consider 10 users per GB as same limit, else you can go with a median of 15 per GB, even at 10 making it 32GB of memory which wont be breaking your bank. Let us know what type of CPU's you came up with, and i'll see what to consider better as not every 8-core CPU is same (different cache's, different QPI & lithography etc), and its not just the RAM and CPU that will determine the performance of your server, you have to find a sweet spot of performance to get the best out of your hardware, and that includes combination of drives, selection and tuning of software etc.
Like for example, you get a server with 8-core and 32GB RAM running on a single magnetic drive of 7200RPM, that wont take you anywhere near to support more than 30 concurrent.