Your options for external filters on a 6g tank are limited pretty much to the above Zoo Med 501 and maybe one other one.
Your options for *useful* internal filters are limited because you are pressed for space in the 6g.
If you don't have a lot of fish in the tank then you probably only need the occasional water change.
Running filterless in your situation is done by simply not putting a filter on the tank.
The pros of going filterless would be: cheaper, less clutter, dead silent, no filter cleanings.
The cons would be: lack of circulation, if you have a lot of fish in the tank you may need the extra biological filtration (depending on how much you fertilize the tank).
The tanks is relatively small at 6 gallons, heavily planted, DIY Co2ed and not highly-lit. If you wanted circulation you could just add an inexpensive pump like the Via Aqua 40 gph (VA-40?) or 80 gph (VA-80) or the 66 gph (VA-60) . Very tiny, very quiet, very low profile, adjustable flow.
"Insanity: doing [or asking] the same thing over and over again and expecting different results."