Hi Proteus, I hope this answer is still valid for you.
To start, lodestone is actually the name for the naturally magnetised version of the mineral magnetite (Fe3O4) which, to answer the second part of your question, is also probably the most widespread (or at least most commonly found at the surface; I don't know crustal abundances of these minerals) magnetic mineral.
Another common magnetic mineral is pyrrhotite (Fe1-xS, where x = 0 through to 0.2). The magnetism of pyrrhotite increases with decreasing iron content. The FeS end-member is called troilite and is non-magnetic (troilite is not a commonly occuring mineral).
Other weakly magnetic minerals that I can think of at the moment include;
Chromite ((Fe, Mg)Cr2O4)
and
Ilmenite (FeTiO3)