The cloudy tank photo looks like a bacterial bloom to me (bacteria are normally too small to filter out, you just need to wait until the rank reaches equilibrium).
How was ?(and how long was) the tank cycled before adding all those fish (were seasoned filters used to properly cycle)?.
Aquarium filters depend on many factors so there is no one best filter for every aquarium. This also depends on what kind of aquatic life you are rising. Here I will explain some facts.
Betta fishes who likely lived in current less water prefer gentle flow from spong filter. As per my experience, this filter need least maintenance cost however they require air pump to work. This makes bit noise depending on build quality. This filter offer biological and mechanical filtration. So keep in mind don't wash them in tap water they need to squeeze every now and again.
The way you describe the whole matter about water filtration it's really appreciatable. Few people like you know that proper method about that. I am really thankful to you. Keep sharing your valuable thaught.