My main objection to the nature of your question has already been dealt with by stoicfury, but I would still like to suggest particular core texts that I feel are thought-provoking, engaging, and worthwhile to read and reflect upon in their own right, with or without introductory texts, summaries, and guides. Subtleties, like stoicfury mentioned, can be missed by even experienced philosophers - but it does not follow that reading primary works (in translation or the original) will not benefit the curious or passionate. Nor does it follow that the best start for a budding philosopher is to avoid primary works in their entirety. Anthologies are good for breadth but not usually for depth into any one thinker's arguments. Anthologies can obfuscate more than clear up the layer of jargon by introducing too many thinkers, each with their own (as well as a shared) diction; anthologies also tend to drop readers in the midst of an argument rather than devote the space to showing how a thinker arrived at the (what may seem to the reader) starting place of an excerpt. Frankly, this is a debate amongst professors of philosophy on how best to introduce and teach their subject and craft to others.
If you understand these reservations but would nonetheless like to proceed with primary texts outside of anthologies, then I would recommend the following as introductions to the field, that also reasonably satisfy the criterion of being a "core" text.
(Also, I'm assuming you mean philosophy in the Western tradition and so will confine my recommendations accordingly.)
I'd recommend reading a few of Plato's dialogues to start. There are plenty of in print and secondhand editions available that collect thematically similar dialogues. They're good, they're short, they make sense even to the lay reader (most of them). Also, if you are serious about pursuing philosophy, then Plato is an author you will have to gain at least some familiarity with. If you feel comfortable and are still interested after acquainting yourself with a few dialogues, I'd recommend moving onward to Plato's Republic.
In the modern era, Descartes' Meditations on First Philosophy is clearly written, again short, and opens up a whole new host of issues that we are still struggling with today.
John Locke's An Essay Concerning Human Understanding is superficially slower going than the above too, though is also cleanly written, and can be understood by an intelligent lay person.
I'll leave it at that, though there are a lot more that are accessible to intelligent, patient people, and many great, exceptional works that may fall outside the traditional "core" of Western pedagogical philosophy. There are also many great histories of philosophy by philosophers (Russell's, Copelston's, Scrunton's, Wildelband's come to mind), which can act as thorough companion guides to most thinkers' contexts and their jargon.