I am glad you are doing your research! Although many opinions here are varied, the true absolute minimum for a betta home is 1 gallon. Starting at 1 gallon, a tank can be properly heated without harsh temperature extremes or fluctuations, can provide JUST enough room for decent exercise, and can be maintained into a workable schedule for water conditions. However, that being said, a 1 gallon is not only the minimum sized tank needed for a betta but it is also the most work for one as well.
1 gallon tanks need to be cleaned more often, with a strict schedule or else you may suffer ammonia spikes and damages. You need a very good heater that is reliable because it is easy to overheat smaller tanks and some heaters are not as easy to regulate temperature, resulting in a more expensive recommended brand being needed. They also cannot have many hiding places in them, which can stress the fish.
This is why most users here will recommend 2 gallons or more for a betta fish. The more gallons you have, the less you have to do water changes. and the more exercise it will get and have more room to hide. Heaters for 2 gallons and up are easy to come by and they can be very attractive set ups.
If you would like to get a betta and not have to do 100% water changes regularly, then I recommend getting a cycled tank. Fish tanks 5 gallons and up are the easiest to cycle and are generally the standard for beginners who are new to cycling. The cycle that is being referred to is the nitrogen cycle, which eliminates the most harmful invisible toxins from the water and converts them into a less dangerous form that can be easily removed with once a week 50% water changes. Not only do you not have to lug a heavy tank around and do a 100% change, but you can do a water change that is less stressful for your fish.
Good luck! Feel free to ask any more questions either on this forum or by sending me a PM. I am always happy to help.