The NTSB will investigate every aircraft accident in the US, and any that foreign authorities delegate to them. As you found, there thousands of accidents ever year. Most of these are not fatal. The NTSB will at least gather the factual information and do their best to arrive at a probable cause.
With limited resources, the NTSB must decide which accidents are important enough to do a major investigation. You can see a map and list of the most important current investigations here, along with the following explanation (emphasis mine):
This listing of investigations includes those open investigations involving accidents or incidents which resulted in significant loss of life, physical damage, involve issues of importance to public safety, or which have generated particular public interest. This represents only a small portion of the investigations conducted by the NTSB, most of which occur at the regional level.
There is no official criteria and not all of the incidents listed will become major investigations that result in full reports. The NTSB will decide based on the situation and factual information whether a full report will be produced. These reports are much more in depth, involve official parties that may submit their own findings and recommendations, and are deliberated on by the board in a public meeting before being officially released along with formal safety recommendations.
The board also periodically releases safety recommendation reports on issues that may not be related to a single major accident, but that are evidenced by multiple accidents that may not have received major reports.
