Here's a whole booklet about exploring beaches.

It says that beach sand has mostly quartz and calcium carbonate as its minerals. You can see some light through grains of quartz. Calcium carbonate is usually white. It comes from sea shells. There are other minerals, too. We used magnets to pick up sand grains containing iron from the sand of some beach in California. Mica is another mineral that can be found in sand. I found it in some river sand in Alaska. Mica is shiny, and grains of mica are made up of stacks of very very thin mineral sheets. The sheets are so thin that there are a million sheets in a piece of mica that's only 1 mm [millimeter] thick.

I would say by far the dominant mineral on typical beaches (re. not carbonate beaches like in the bahamas) is quartz. This is the same mineral that can be made into glass, however, on beaches it's not sharp because millions of years of weathering and erosion and re-working from waves makes the sand grains small and rounded. But yes, depending how well sorted a beach is (dependent on how much wave action there is on the beach and source of the sediments material), there may also be calcite (carbonate from shells) and what we call "lithic fragments" (any other mineral that's been ground up and has survived weathering).