Any handheld camera is fine as long as the photos are overlapping!
This is the way for art object conservation and digitization.
Actually, we do have actually lots of nice examples of 3D models of objects captured from a handheld camera, including mobile phone cameras. You may search for "object" to view these models.
It usually requires lots of photos to build a complete 3D model. It might be tedious to use a handheld camera to capture photos.
We recommend to use a drone as a drone automates the capturing and a drone can fly higher to be able to see the object from all angles!
To capture a small-scale object, some people often uses a turn-table by placing the object on the table. This is equivalent to the circular POI flight of a drone for an outdoor building.
To capture a face, we often uses an array of synchronized cameras, placed in front and around the person, from a few to a dozen of cameras, to avoid any undesirable movements during the capturing.
Last but not least, transparent, highly reflective, and glossy objects (non-lambertian materials) are not good at all!