How to Clean Water??

This may be a silly post but I've done some research and just got more confused. Basically, I want to experiment with Mycorrhizal for my next grow and need to remove all the bad stuff from my tap water. Historically I've used tap water, left out for 24 hours to breath, then PH adjusted with ph down. But now my understanding is all the chlorine and other junk needs to go. I'm not going reverse cartwheel backflip osmosis or any of the other advanced water systems. I want as simple as possible. I'm even thinking of just rocking Brita and constantly filling my watering containers throughout the day until I have enough... but this is very inefficient. Are there any other options? Is there a carbon filter funnel? I have a fancy tap in my kitchen... can I install a filter under the counter? How do I "clean" my water cheap and easy?? Thoughts anyone?

Tap water is fine. Chlorine and all. Read up. Or not.

The big boy filter has both a carbon and a sediment filter. I used one for a while when I was in a fracking area and my water was crap.

You can get one on Craigslist cheap but the filter are about 100 for both.