A betta or a guppy are good candidates for this kind of setup, but try to have a container with at least 2 gallons. The bowl I used here held 2.6 gallons empty. If you are keeping a betta I'd definitely get a heater, since
IMO they do not do as well in room temperature tanks, in spite of how commonly they are kept this way. Guppies can tolerate cooler temps much better.
I probably did not need to use a heater for mine but I was worried about some of the plants, so I got a Hydor 7w heater, which is basically a small mat about the size of a playing card, which can be suction-cupped to the side of a small tank or buried under the substrate. There is no thermostat, but it raises the temp a few degrees. It heated the water too much in my bowl when it was in the water, but I buried it under the substrate and now it keeps the tank a steady 78. The plants have grown up and hide the cord. My bowl is pretty high tech with strong light and heat, but you do not have to bother with either, and go completely natural.
If you want something easy, get some sort of bowl or small tank (I like the seamless look of bowls, personally) and use some coarse sand as substrate. Tie some java moss and/or java fern and stick it in there with a pretty guppy. Place this on your desk with a fluorescent desk lamp, on a table under a table lamp that has a screw-in fluoro bulb, or even just on a counter in a reasonably sunny room. That is it. You could put it anywhere you would put a house plant. The plants will grow even with ambient light from the room. I have a friend who has a bowl like that in her windowless bathroom, and the only light comes from a decorative lamp on the counter that is on a timer. The java fern grows fine and the guppy appears happy as can be.
Change the water every 2 or 3 days, even every day when it is first set up. I have a Solo plastic cup I use to scoop out about half of the water, then add new water with the same cup, with a couple of drops of Wardley's dechlorinator. Nutrients and waste build up quickly in a tank like this, so once a week I use a tiny gravel vac I got at Walmart, and take a pass over the substrate.
That is it. Maintenance takes mere minutes, and since mine is in the bathroom it is even simpler - the sink is right there.