Few comments:
For all but really problem water, a softener from Amazon or a big box retailer works fine. You pay those dealers for service and expertise. For complicated water (lots of iron, sulphur, pH) often additional filters might be needed, or special softeners that can contain different media types. A dealer is a good reference in those situations. A standard softener can handle small amounts of iron, etc but as mentioned should be treated with extra cleaner occasionally.
The amount of salt added to your intake daily is roughly the same as eating a slice of wheat bread, so only truly a little concern for the worst off individuals.
Most standard softeners have a 1" npt threaded connection that you can adapt or plumb to your plumbing.
Separate brine cabinet doesn't change anything about operation. Makes it easier to clean out if you use crappy dirty salt, but that's rare. Single cabinet units just take up less space.
Don't be too wrapped in max capacity, since almost nobody uses that when it's actually programed and is really inefficient with salt use at the highest settings.
That small unit mentioned is a water "conditioner"/ scale prevention device. These treat the water so minerals don't stick to plumbing, but they don't remove anything from the water.