Tank: 2.5 gallon or bigger. I personally like 10 gallons split in two by a divider so I can house two bettas next to each other. Make sure you have a lid, or something to go over the tank. Bettas jump!
Water: Use tap water, but you need a water conditioner from the stores. Get one that removes both chlorine and chloramine.
Heater: Depending upon the size of the tank you get, depends on the size of the heater you'll want. Get one that has adjustable temp. 2.5 - 5 gallon tank = 25 watt heater. Anything bigger, like a 10 gallon, get a 50 watt heater. There is such a variety of heater brands out there that differs by location I won't really give you a brand, since your stores may not even carry what I have around here.
Tank decorations: Optional, but your betta will definitely appreciate not having a plain tank, and so will you, because a plain tank just isn't as pretty. Substrate goes in here too. It's also optional. Some people prefer bare bottom tanks, they are generally easier to clean. Some fake plants, or a castle or cave can help spruce up the betta's home. Don't get any decorations with sharp edges, as bettas will catch thier big fins on these and tear them. If you feel adveturous, try a real plant or two, but those alsoo require a light.
Food: Get betta pellets. Make sure they contain more meat than veggie matter (look on the ingredients label, if wheat, plant matter, flour or soy meal are the first things listed, don't get it). Bettas are carnivores, and can't digest veggies very well. How much each betta eats varies ona ctivity level and size I'd say. But a lot of people feed 2-4 pellets twice a day, so that's a total of four to eight pellets a day. If the betta doesn't consume the food, remove it from the tank and consider lowering the amount of food you feed each day.
Yes, bettas must be able to reach the surface of the water to breath, this is what their labyrinth organ is for. They breathe air from the surface, so don't cover the surface of the water (those 'peace lily' vases they stick bettas in are terrible for the fish).
Don't stick your tank in the sun, you will get an algae bloom and I assure you, you will not like it. Neither will the betta. The tank needs an artificial light source. Either get a hoood for the tank that you can put a light in, or mount a light to the tank - those clip on flourescent lights you can often find in Home Depot or Lowe's work nicely. Or, if the are in a room that has a light on all day, they can go without a dedicated tank light, but they do need some light.
Good luck in your betta hunt on Sunday!