Sandstone is a category of rock made from sediment (a sedimentary rock). The sediment particles are clasts, or pieces, of minerals and fragments of rock, thus sandstone is a clastic sedimentary rock. It is composed mostly of sand, which means particles of a medium size, so sandstone is a medium-grained clastic sedimentary rock. More precisely, sand is between 1/16 millimeter and 2 mm in size (silt is finer and gravel is coarser). Sandstone may include finer and coarser material and still be called sandstone, but if it includes more than 30 percent grains of gravel, cobble or boulder size it's classified instead as conglomerate or breccia (together these are called rudites).
Sandstone has two different kinds of material in it besides the sediment particles: matrix and cement. Matrix is the fine-grained stuff (silt and clay size) that was in the sediment along with the sand whereas cement is the mineral matter, introduced later, that binds the sediment into rock.
Sandstone with a lot of matrix is called poorly sorted. If matrix amounts to more than 10 percent of the rock, it is called a wacke ("wacky"). A well-sorted sandstone (little matrix) with little cement is called an arenite. Another way to look at it is that wacke is dirty and arenite is clean.
You may notice that none of this discussion mentions any particular minerals, just a certain particle size. But in fact, minerals matter.