Water additions and knowing your water are one of those things that will just help improve your beer - noticeably at that.
I know you said you do not care to buy distilled water and I'm not intending to change your mind. All I'll say is that is what I do and it isn't that bad. I have to go to the LHBS to pickup supplies and I stop at the store by my house and grab 10-12 gallons of distilled water.
There are other options. You could buy an RO filter for your house. Lots of people do this. I opted not to do this as it seems more of a hassle than going 5 minutes to buy distilled water. I think you could use something like
this.
I can't comment on whether or not a screw on filter for the end of your hose would do you any good, as I do not know. All I can tell you is water plays a huge part in the beer.
My recommendation to you would be to get your water tested. If your water comes back and looks to be suitable for brewing with some extra additions on your brew day, you've saved a bit of work.
In answer to your question about how can you make sure you're doing the necessary stuff to your water - right now, you can't. In order to know you're doing the right stuff, you'd have to know what's in your water. That's why I buy the distilled - I know that there is literally nothing in that water, so it's a blank canvas for me to make the profile.
On the other hand, if you aren't that picky about your water and the beer your brewing is good to you and you like it, I suppose you don't have to do anything differently. All depends on how technical you want to get.