I would say that the safest route for plants (espescially in an uncycled tank) would be java fern, java moss and anubias.
1) They are all low light plants.
I have had success with them under low light and even no light. The flourescent that comes with your 20g (hopefully) will totally support them. You should also be able to buy a regular screw-in 'Power Saver' bulb that will fit the hood of your 2 gallon. If your 2 gallon didn't come with a hood, the plants should be okay under low light or even no light. One option is to use an ordinary desk lamp with a power smart bulb.
2) You don't need heavy fertiliser and/or a specialty substrate for them.
Some plants are heavy root feeders and pretty much need to be planted in something like Eco-Complete or Flourite. Their root systems also don't take well to being taken out every time you clean.
The plants I mentioned, however, will actually get rotten roots if buried in the substrate, therefore can be taken out of the tank for cleanings with absolutely no problem. Additionally, they can easily get their boost from a liquid fertiliser because their roots are not covered up by gravel, wheras most plants depend on root systems in the substrate to absorb nutrients from all the waste in the gravel.
3) They can be easily rooted onto driftwood or rocks. In fact, its preferable for them. This will also also make it alot easier for you to clean your tank, as you can just pull the driftwood out with all the plants on it for cleaning. Also, it looks really nice and you won't have to worry about arranging each individual plant every time you put them back in your tank. Just drop 'em in and POOF-- instant aquascaping! It's also easier to rearrange the pieces of driftwood to switch it up for your betta.
Good luck and hope I was helpful!