Unfortunately, nothing much, but perhaps 1 smallish goldfish, but only for a short period of time, if you know what you are doing you might get buy. However, they are generally very messy eaters and thus make poor H20 quality fast, Most all species of these fish will grow far too big for a 1 gal tank but some will grow so slowly that it might not be an issue for some time. However, with only a gallon, I do not recommend them. In a 1 gal situation a male fighting fish may work or any of the small Labyrinth fishes. These are fish from southeast Asian region that generally live at times in mud puddles during the monsoon periods of flooding and are thus happy in small spaces, because they breath air, H20 quality can be slightly marginalized but never neglected. If the tank is <11 inches high a male beta or Paradise fish (which can be absolutely beautiful), Cherry Red Shimp can work quite well if you can find them and even 1 small crayfish may be suitable, although you will have to clean up after it alot, and will have to feed live food, lots of work, too much, so why not upgrade to a small 5 gal tank and follow my instructions below.
As long as the Bio load is not compromised this is smallest tank you can have. It's small size should no be an issue for someone who knows what they are doing, I have an unheated 5 gallon tank in my kitchen, that contains 2 Zebra Danios and 2 Cardinal Tetras and 1 Cory Cat and all have been alive and well for 3 years, the rule of 1 inch of fish body per gallon of water works, but you have to play by the rules of nature.
This tank ran for 6 months 1st with only snails and a small amount of biological starter. Once the filer floss is dark green and covered with biological matter that looks like algae, do not change it, worship the **** out of that because its more powerful than any new canister, uv, reverse osmosis crap that anyone will sell you, in fresh water conditions its all about aeration and water movement.
When the water smells like rainwater on dirt in Spring you can stock the tank to the levels I describe above. I never change the water only top it off with matched water of similar temp and chemistry as it evaporates about 1x per month. The filter floss material is seldom changed but the carbon is about every month or two. I feed 1x per week only! Agitate the substrate 1x per week and use a power filter designed for a tank 2 or 3 times bigger to have maximum water filtration the overturns the tank volumes between 3x and 5 x and hour. A small power head on the other side of the tank form the filter at the bottom will create a circular current which you need in any tank and especially a salt tank. Also, keep the lights off ! No more than 2 or 3 hours a day otherwise you will turn your water green, also if you do have a light make sure you are not using an incandescent bulb as may 5 gallon tanks come with or offer this kind of lighting and that kind light source will only over heat the water, screw up the H20 chemistry and fry your fish, replace the incandescent with compact fluorescents that produce similar Lumens’ at about ¼ of the wattage .
You want to keep your small freshwater tank as cool as you can, this is a good rule for any species to keep metabolic rates high, this also coincides with weekly feedings. Also, when stocking try and pick small fish that swim in different levels of the tank, for a 5 gallon tank the fish should have an adult body from head and tail of no more than 1 inch.
Substrate can be off the shelf bleached sand or crushed stone med or fine aggregate, sorry generally plants can only be plastic in this scenario. If you are more advanced there are 2 or 3 species of common potted hydro folia that can work but you will need to build a more robust lighting cover with 2 macro fluorescent tubes and will thus have to pay more attention to water quality If a beginner is patient enough, this can work out fine. Best of luck!
