If you don't know what the core/essential texts are, in my opinion you are ill-equipped to read them alone, unless you are the next Einstein or something. Even otherwise very advanced readers who are new to philosophy can completely miss the subtleties of philosophical literature, particularly literature that is either not from our current era or writing that has been translated from another language (or both). There will likely be jargon and phrases you are not familiar with, in many cases which you won't be able to easily look up on Google.
Accordingly, I would strongly recommend starting with a solid introductory book before you dive into them such that you can acquire a firm grasp of the basic concepts you will need to know. Some authors are of course easier to read than others, but however you slice it, you want to be on level 1 before you get to level 2, and that means acquiring an introductory understanding of philosophy before you dive into some of the more classic texts.
As for the "core/essential texts", it's not exactly a simple task to just sum up all the texts we've read and provide a list, especially a list that's in a good order because in many cases order does matter. But more importantly, it's not often necessary or even useful at times to read the entirety of a particular text; in fact, it can even be off-putting and seriously diminish your interest in philosophy if you force yourself to read the whole of a particularly bland text. For example, I've read the whole of The Critique of Pure Reason, and while many would probably agree that it is an essential/core text, I would not recommend reading the whole thing unless you plan on being a Kantian scholar (I had to read it for a class). It just gets too dry in parts and honestly, even classic texts will have sections which will not be very exciting for you — trust me, no one finds all of philosophy interesting and cool.
The easiest (and "safest") way to get a solid grip on the core texts of philosophy would be to just buy an anthology for each major subfield of philosophy. Often these anthologies have the relevant texts annotated to help with clarity, and omit much of the unnecessary sections which you would otherwise pointlessly labor through. This will save you a lot of time both in reading but also in understanding what's important to understand, and then if you find a particular text/subject really interesting, you can always get the full text later.