Bare minimum betta tank is more like 2 gals if you do some research on them. I've kept bettas and like them and as far as quality of life, a lot of people don't realize how intelligent bettas are, they need more than just a bare bones environment to be 'happy', they're among the more interesting and interactive fish you can keep if you give them an appropriate environment and are observant. It's something of a misconception that bettas normally live in tiny puddles, sometimes they get trapped in a tiny puddle, but that doesn't make it their natural habitat, which may be shallow but is also spread out, like a rice paddy for instance.
To do a micro tank you need micro fish, something an inch or less adult size. Trouble with a lot of these is they're shoaling fish, some tetras and rasboras, for example. Or there are others that are rare in the hobby.
Plants and a small, colorful shrimp is probably one of your better options to go that small. Yes, there are tiny fish that people do in tiny tanks but it's typically more of a specialized niche in the hobby, relatively skilled specialists, not someone new in the hobby. You'd want to search something like "micro tank aquarium" or "nano tank" to see examples. Even then you'd want to distinguish between something viable and a novelty act that would be unkind to the fish. A good micro tank would still need a filter in most cases, which is why they make 'micro' or 'nano' filters.
All in all I'd agree with the suggestion to go a little bigger, more like 2.5 gal at least and 5 or 10 would be better to give yourself better options for fish and make the tank easier to keep healthy.
