This is one of those questions that has a lot of possible answers.
The first thing you are going to need to do is get your water analyzed so you know if you have a problem in the first place. What is your TDS reading on the existing water? Are you on a well or a city water system? A city water system contains chlorine. A well system does not.
Just an FYI, the guy that sells the water system is not always the best guy to give you an unbiased opinion. All water has something in it. That does not necessarily mean that that the water is bad. Your local county health department usually can test your water if you provide them a sample. The cost is about $20-$30. You would need to call them for instructions on how to do this.
You need to understand that you use water in many different ways in your house. You will want to treat your water differently for each type of application. (if you need to treat it at all)
If you are on a well, sometimes a simple filter system installed at the point of entry (like a garage) will remove any sediment that is getting into the system. That is the simplest solution.
You drink and cook with water. That water needs to be the purest water of all. It is usually treated with a reverse osmosis system which is placed under the kitchen sink. It makes 7-20 gallons a day depending on how much you use. You'll want to remove the chlorine out of this water. You don't need to treat the whole house with a reverse osmosis system. A reverse osmosis system is not generally used on well water for reasons that I will not go into here.
There is water used to wash clothes. That water is treated in a different way. You don't not need to remove chlorine out of this water, but you might need to add a water softener if your water is bad. Most of the time, you don't need to do anything unless you have a problem. A water softener adds salt to the water to "soften" it while running the water though sediment filters that need to be changed on a regular basis.
There is water used for showering. That water is also treated in a different way. Sometimes a point of use catalytic system on the shower head will treat that water. You will want to remove the chlorine out of this water.
Water treatment systems will require regular maintenance no matter which one you use. If you don't maintain them, then you will find they will clog up and you won't have any water at all.