Yep, bettas don't need super big tanks, but 2.5 gallons is the smallest you can go. Perhaps 1 gallon might be okay in some cases, but since you're a beginner, bigger is better since they are less maintenance.
Betta fish of course need a heater, since they're tropical. Filters are optional, sometimes they can have too much current and betta fish may struggle to swim. However if you have a 5 gallon tank or larger, it's recommended you get one, but make sure you get an very gentle filter. If your tank is smaller, i recommend you get a sponge filter.
Air pumps are not needed. Betta fish can live in waters with little oxygen, however if you want to you can get them.
For water changes, do 25% - 50% each week for filtered tanks. For unfiltered, you may have to do more and larger percentages.
Betta fish love plants (especially live) and caves. Adding decorations or plants will make your fish feel safe, but no plastic ones since they can rip their fins!
I also recommend having a "first aid" kit for your betta fish, in case she/he gets sick. You're probably thinking "Why buy one now?"
Well, you may not find the needed medications and may need to order online, and by then it might be too late. :(
For the first aid kit, you need . .
AQUARIUM SALT - Even though bettas are freshwater, aquarium salt can help with nearly every illness. (except for dropsy) But remember to only use if there's sickness because too many will harm your fish.
EPSOM SALT - Epsom salt helps get fluids out. It's good for bloating and constipation. (also helps a little with dropsy . . but there's a very rare chance your betta will get that.)
INDIAN ALMOND LEAVES - Indian almond leaves have lots of health benefits. They can calm down your fish, and you can use it for general health. Be warned that it releases tannin, which can make your water look brown.
Also, get a medication which treats a wide variety of diseases such as maracyn. However, you should try out the more natural methods listen above first.
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