filterless five gallon
The key is your plants have to be growing really well, then they clean the water. I bubbled a tiny tiny bit of C02 into a five gallon through a limewood airstone near the surface to drive plant growth, but it can be done without C02 too. You should set it up as a plant only tank and wait for them to grow a month or two, and test the water.
Hardy fish like white clouds, killies, or a betta are a good idea. You should probably have around three small fish max so a trio of killies is very nice. Nothing like danios that need swimming space. Maybe you could have 5 neons with no corys. Corys are more sensitive to water quality. I had six rasbora maculata in a mini tank and that was beautiful-but that one had a mini filter too.
Unless you keep your home at 75 degrees you may want to purchase a hydor 7.5 watt mini heater. They are so cool, small and flat. You can't adjust it but it kept my tanks around 75. Most tropical fish and many plants like it warm. White clouds and some killies will tolerate it cooler, but not the neons. Bettas actually hate to be cold, if you give a betta a heater he will perk right up.
Fast growing stem plants are good to include since they grow fast enough to clean the water. You regularly pull them up and replant the tops. I've had success using a couple of 14 or 20 watt compact fluorescent screw in bulbs for light.
Good luck, it is so fun creating a mini-world!