Betta pellets are better for them than flakes. Make sure to only feed 3-4 pellets a day with one day off for fasting so they can clean out their system. There are 5-gallon kits at WalMart and PetSmart that go for less than 40 dollars. These come with a lid/hood.
I have a 10 gallon tank with a betta in it, but instead of having an actual hood, I have a piece of screen on a wood frame over my tank with a spot cut out for my filter. Bettas can be jumpers, and you wouldn't want to find a dead betta when you get home.
I have a cascade filter.. AquaTech 2-10, or 5-15 I believe. I just have a piece of a soda bottle blocking part of the cascade so the current isn't so strong. The only thing you hear is the cascade hitting the water.
EDIT: Phansie, bettas are tropical fish. The only situation in which you wouldn't need a heater is if the room temperature stays at at least 78 degrees Fahrenheit. I live in Puerto Rico, so I don't need a heater (this is a tropical island). The nitrogen cycle is necessary for any fish, as ammonia, nitrite and nitrate is toxic to all fish. Your sister's betta is alive, but not necessarily happy. The filter holds the bacteria necessary for the tank.
EDIT2: Also, a gravel siphon and a thermometer. I got a thermometer for 2 bucks at WalMart and the siphon was 7ish. Vacuum/siphon your gravel in thirds. Every time I do a water change, I vacuum 1/3 of the gravel to get the poop out.
