I can see that you desparetely want to have fish in your tank. My first suggestion would have been the betta as they can breath the air we do and do not rely on oxygenated water. You are extremely limited to the type of fish you can get without a filter, as the filter not only cleans the water but also provides good oxygenation of the water - so the water is continuously flows.
Stay away from angel fish or anything that will out grow your tank. One gallon per inch of fish is the rule (once they grow up). I don't belive that your set up will meet the needs of this beautiful fish. You could try guppies or gold fish...gold fish have lived many years in little gold fish bowls. Nothing fancy though, just gold fish.
I would stick with fish that stay small and are hardy. You will still be faced with the murkey waters and regular cleaning of your tank will have to take place 25% every other day to ensure proper water values.
Or, you could get newts or something like that...I have seen them in pet store in small tanks, but again research them to see if they will outgrow your tank.
Good Luck and I will keep an eye out for something else to suggest to you.