Given nothing else around this tank I'm thinking it might be marble chips (or there used to be marble chips, depending on how long it's been neglected) to neutralize acid water and keep it from eating pipes and old leaded solder joints.
As for what, if anything, to replace it with - get a laboratory test done on the un-treated water straight from the well (you might have a minimal one from the time of purchase, but the most minimal one really only tells you if it's got bad bacteria or not.) When you know what it has got in it, you'll know what to treat for.
There is no "standard" filter system because wells produce water that may need no treatment at all, a little bit of treatment, or a whole lot of treatment, depending what the water they are drawing from has in it. And there are choices of different ways to treat various issues that water in need of treatment may have.
I've lived with wells all the way from "tests very nearly like distilled water" to heavy black sulfur, significant iron, and extremely hard. They need different things done to them to make the water acceptable, though I ended up just hauling drinking and cooking water at the black sulfur well house.
While you can try to DIY testing with test strips, my experience is that an actual lab test (or a colorimetric test at a well-equipped plumbing department, for the things they test for) is far more reliable. You could reasonably expect to get a ballpark on pH that way. But that's only one of many potential things to deal with.