What is the best water for fighting fishes?

Fishbowls are not really meant to have any fish in them even though places sell them like that.
The only fish that could live in something that is 2.5 to 5 gallons in size would be one betta fish.
The water you use will depend on what your tap water is like - so you should test it first, and make sure that you always use the recommended dosage of water conditioner.