Definitely not goldfish! Goldfish get huge and need 30+ gallons. Honestly, putting any fish in a container under 5 gallons is pushing it, so I'd look for a 4-5 gallon bowl if you can find one. Otherwise, make sure to stay on top of water changes.
I'm not super familiar with the person you're referring to on YouTube, but many people (including me) have done dirted bowls/nano tanks with great success. Look up "Foo the Flowerhorn" on youtube, he has videos that give a great breakdown of the process. The key is to cap the soil with at least 1 inch of gravel so that it doesn't dirty the water column, and wait at least 1-2 months for the aquarium to balance out before adding livestock.
For a betta tank, you won't need RODI water unless you've got some crazy tap water. If your pH is between 6 and 8, you should be good. Plants tend to prefer a slightly lower pH, but soil tends to decrease pH, and many commercially available substrates do this too. Betta tanks do need a heater, but you can get some pretty small ones at your LFS.
Many fish stores will stock the plants you mention, but if they don't, online is also a good option. Be sure to research the lighting and co2 requirements of each plant you're interested in, as there's quite a range. If you're planning on going co2, I'll let someone else chime in, as I have zero experience with co2 setups. But some great plants which require only moderate lighting and no co2 are: dwarf hairgrass, sagittaria subulata, vallisneria, anubias, hornwort, cryptocoryne, and many stem plants (hygrophila, rotala, etc)