In general only the ferrite group :

iron, nickel, cobalt.

Other material may be alloyed with these, but the ferrite group is essential.

The term alnico is derived from the names of three metals, aluminum, nickel, and cobalt, which can be used to make an alloy that has useful magnetic properties. Ferrite is a form of iron. Alnico magnets are more powerful and more expensive than ferrite magnets.

Ferrite

A good magnet should do the trick. Neodymium-Ferrite-Boron magnets are a good candidate.

Yes, we can see the use of iron oxide (the Fe2O3 kind, which is iron (III) oxide) used in magnets. There are a number of different things that could be used in a magnet, but simply using this material, often referred to as ferrite, and a little bit of some other materials to make up the ferrite, will allow for the construction of a magnet.