New to water softening/treatment options.

My wife and I just bought a newly built home and we are interested in looking at water treatment options for our house. We really have no clue about water softeners and the pros/cons of installing them.

Does anyone have any thoughts and opinions on whether or not they are worth it and what kind of system to get?

We know there is something wrong with our water because it tastes horrible and leaves white spots galore on the glass shower walls. But really have no idea how to even go about figuring out what water filtration is needed.

Thanks for any advice.