If oxygenation is an issue, I have played around with flushing barrel filters too. This is where the water level slowly rises inside the filter and then dumps (to create a surge wave into the tank). With rising water, every single bit of your media gets wet/used without a water distribution tray or filter media channeling. And all the old air is expelled and new air pulled in each cycle.
I sometimes use this as the final filter after other barrel filters. Just set the internal water height a little lower than the others.
It doesn't really matter which type you opt for as long as you are happy with the results.