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One problem that I'm worried about is plugins changing Core files.

Ship your Core files as a signed PHP Archive.

I'm trying to limit plugins access to either the files or php functions. It would be great if plugins were only allowed to use Core classes/methods.

That's a very challenging problem to solve, and is far beyond the scope of a StackOverflow answer. At a minimum, you need to make sure that the server bootstrapping hits your framework (which works out well if you're using a signed .phar rather than a mutable .php file).

However, beyond that, you cannot stop plugins from calling PHP functions in the standard library. An alternative approach may be to build a Template engine (e.g. like Twig) and only let plugins be written in your own domain-specific language that cannot call arbitrary PHP functions, only the ones you provide.