To get rid of hard water you need a water softener not a filter.
I use a GE SmartWater whole house filter with a five micron charcoal filter cartridge followed by a
Mark 8000 water softener. It's very similar to the popular "On-The-Go" Portable Water Softener but was cheaper when I was shopping ($240 including shipping).
I got the filter and hose fittings at Home Depot - about $25 for the filter, I don't remember what I paid for the hose fittings. The cartridges cost about $7 each and last two to four months depending on water quality.
Having the filter before the softener keeps particulate matter out of the softener medium.
I also have both units set up with quick disconnects. I use water test strips to check the hardness and don't connect the softener when it isn't needed. I always use the filter.