You would want the iron filter system before the water softener.
The iron filter will not take care of the manganese.
Here is a solution that will take out both iron and manganese:
http://www.waterfilters.net/Iron-Manganese-Whole-House-Filter-W-410-CFM_p_0-497.html
However, your manganese problem is probably not severe enough to justify this system. The iron filter will probably reduce some of your manganese anyway.
To remove the hardness, you could use these cartridges:
http://www.waterfilters.net/Pentek/wholehouse/Specialty_Filters/WS-20BB-Water-Filter.htm
Thank you,
WaterFilters.NET