If your pieces have individual (non-spatial) attributes, such as when the piece was found, an important number for the piece, or who found that piece, then you should use POINT geometry and then each POINT can have its own attributes.
Otherwise if the pieces are never going to have any individual characteristics that you want to put in your data, you can use MULTIPOINT. This would make it simpler to do a 1-point-to-1-row join between spatial data and a spreadsheet.
You can split MULTIPOINT to POINT with a QGIS process and I think it will replicate the MULTIPOINT attributes across each POINT created.
I've never really understood why the OGC SF standard has "MULTIPOINT" since it can always be equivalent to a POINT geometry and an N-points-to-1-row key to a database table to define the collection of points that would otherwise make up a MULTIPOINT, plus you can have individual POINT attributes too.