The answer to your question is kind of long, but fairly simple.
In the simplest terms, the dimensions of your aquarium should be tailored to the fish you wish to keep and, all things being equal, an aquarium with the same gallon rating as another one but with a larger surface area will usually be better.
You're betta's pretty small (relatively speaking) and so a lot of the decision is up to you and can be dictated by what sort of space you have. If you find that having something tall and narrow is better in terms of space for you, your betta won't complain. Likewise, if you had a tall, skinny fish a tall, skinny tank might be recommended (think Angelfish).
The reason the surface area is important is that it allows for gas exchange between the air and the water in the tank. This somewhat increases carrying capacity and so a 20 long will have a marginally higher carrying capacity than a standard 20.
Tall, skinny tanks are often referred to as "show tanks". They look especially pleasing to the eye. Meanwhile long, low tanks are referred to as "breeders" because they provided that gas exchange for the fish.
It doesn't matter as much as it seems it might as long as you have enough volume for the fish you're keeping. Your betta would be very happy in any of the tanks you mentioned from the 5.5 up through the 20. Larger volumes of water are easier to keep stable (pH, nitrates, ammonia, temp etc take longer to change dramatically) but there are plenty of people who first learned on a 5.5g or a 10g.
If it was me, I'd be really tempted to grab the 10hex, plant it nicely, and get a group of corys or something for the bottom. The betta makes finding compatible tankmates a bit difficult, especially in a small tank. But the corys hang out on the bottom and the betta will stay in the middle-top.
Good luck, and ask questions. Sorry the answer was so long.