A quarter gallon vase is going to need to be cleaned every 1-2 days in order for the bettas to remain healthy. A small amount of water like this goes toxic very quickly because the fishes droppings causes a build up of ammonia in the water and ammonia is toxic to fish. Another problem is that it would be very difficult to maintain a stable water temperature in a vase so small.
Bettas are tropical fish ans like all tropical fish they require a stable water temperature to survive, fluctuations in water temperatures cause the fish extreme stress and in turn compromises their immune system putting them at risk of all sorts of horrible and often fatal diseases. The only way to provide a constant stable temperature for your fish is buy using fish tank heaters that have a thermostat.
As a bare minimum of equipment goes in order to keep your fish healthy I would have to recommend that you supply your bettas with tanks of 2.5 gallons and a heater each. Your would also need a water conditioner that removes chlorine, ammonia and heavy metals. Any good quality floating betta pellet will suit your fish, I use Hikari betta bio-gold pellets which they seem to like.
Good luck with your new bettas
and if you need any more advice don't hesitate to ask we are always happy to help. By the way we would love to see some photos of your bettas.