You don’t have to use maya. There several alternatives, though they useage might vary depending on fbx level support.
- Blender is free alternative, though AFAIK it have it’s issues with exporting skeletal meshes and animations in FBX.
- modo is another alternative though it is not free, it’s far cheaper than maya. It have pretty nice animation and rigging tools. The issue is that FBX support is average at best (at least with UE4). There is axis conversion issue, and edge breaking so it might pose issues.
- 3ds max. Well, not much to say. It’s on maya price level, you can just as well use maya.
I haven’t used other packages, so I can’t tell. But as long as you can export animation into fbx file it should be good.