Sorry but some of the advice you are being given is sooooooooooooooooooooooooo Outdated it is unbelievable.
There are now so many options available for smaller tanks, from what was known.
Ok, so it is just over 3Gallons. You are not limited in the fish yo can now keep in that size as the variety has increased.
Yes the norm is a Fighter and some endlers.
Have a look on here >> lists sooooo many Nano/Pico Sized fish
Minifish .
I have Been Keeping nano/pico sized tanks for a few years now and have gained experience of what fish are most suitable.
I have a 1G Pico, It is Planted with HC, Riccia, Amazon Frogbit, Azolla, Duckweed, Pennywort. It is Heavily filtered using a Canister Filter. The Inhabitants: 7 Chilli Rasboras, 20+ Cherry Shrimp, 3 Tri-Horned Nerite Snails, Countless Ramshorn Snails.
Tank Number 2:
6.2G, Heavily Planted, Heavily Filtered using an Azoo 240 Mignon HOB Filter.
Ihabitants: Trio of Platinum Halbeaks, 20 Gold/Wild Heterandria Formosa, 10 Threadfin Rainbows, Trio of SB Rams, 20 Red Coral Platties, 2 Stiphodon Gobies, 2 Gold BN Plecs, 1 Amano Shrimp, Dunno How Many Mixed Dwarf Shrimps, Cherries etc. And fry from the Platties, HF, and Snails.
Now I do not have any probs with the above tanks, and they are very active looking.
Many people Keep Pico/Nano Tanks and they are more colorful and exciting to watch then some larger tanks. Small tanks are a challenge to both Scape and balance. Now the tank you have has a Filter Suitable for keeping a few different Options. I have used this filter before and it is Very Very Good at it job.
You could Keep and Lovely group of some of the Rasboras and then a Few Gobies and a plec. As you gain knowledge and understanding of the requirements for smaller tanks, you willbe able to become more adventourous with the stocking. Ofcourse you may need to upgrade the filtration to a larger filter the more inhabitants you would want to add.
I would Suggest reading the planted section, as you can add more inhabitants the greater the amount of plants used and the types.
E.g Amazon frogbit is a Very Very hungry plant and is great for smaller tanks, as it absorbs ALOT of Nutrients from the water.
Also there are great resources on the net in other forums that specialise in nano planted tanks.
But, saying all the above, It depends on what you want to keep, Planted or Not.
If not then it limits what you can keep to the more hardier fish that are not that fussy on water conditions. E.g Gouramies, Tetras, Platties etc.