Why the format matters
The format decides which information travels with the geometry. A simple part and a complex colour project have different requirements.
STL
STL describes the model surface with triangles. It is simple and widely supported, so it remains a common choice for printing.
OBJ
OBJ also stores mesh geometry and can use linked materials and textures. It is convenient when models move between 3D tools.
3MF
3MF is a modern container that can store units and extra information about the model. What it can do depends on the particular software.
What to choose
If a workshop or a program requires a particular format, it is better to follow that requirement. STL often suits simple geometry; OBJ or 3MF are useful for richer data.
A format does not repair a model
Before printing, the scale, surface integrity, thicknesses and whether the part can be manufactured still need to be checked.