I installed an iSpring WGB22B 2 stage whole house system. My well water flows through the first stage sediment filter, then a charcoal block filter. Fairly straightforward DIY install in my basement just after the water holding tank. Pretty satisfied for our needs.
Faced with poor quality tap water, I don't think a filter is going to do very much honestly. RO water takes away all of the minerals so that's no good either in my opinion.
I'm lucky to live in a country with top quality tap water that doesn't even need chlorine because the standard is so high.
However, if I were in your position, I think I would stick to bottled water and buy the largest quantity containers/bottles available.
Unfortunately there is no right answer. A realy good one is super complicated and takes everything out of the water. Including the good stuff. Anything less than that and it`s pretty much a shot in the dark.