I prefer the 5.5 gallons from Petco. Getting the bare tank lets you choose which filter, heater, and light yourself. There are also kits that choose filters and lights for you if it's overwhelming.
I prefer 25 watt hydor theo heater, online on Amazon. Basically, you'll need 5 watts/gallon to heat the tank correctly. You may need more if your home is too cold. Make sure it's adjustable!
I prefer live or silk plants, up to you. There are many varieties of low light beginner plants that can be tied to rocks or rooted in gravel or sand. They grow well with a clip-on lamp with a daylight colored compact florescent bulb. Silk plants can be planted in the substrate and floated on the surface. Either way, make your tank into a jungle to have the happiest fish.
sand or gravel are the simplest
There are a variety of filters available. I prefer sponge filters and internal filters over hang over the back filters. I have this sponge filter, and it works great for 5.5 gallon tanks http://www.amazon.com/gp/product/B00...ilpage_o05_s00
It needs http://www.amazon.com/gp/product/B00...ilpage_o00_s00
to run it with some airline tubing and a valve that keeps the water from backing into the air pump if the power goes off.
For internal filters http://www.amazon.com/gp/product/B00...ilpage_o03_s00
this is great. You can point the spray bar at the wall, so you get water movement without pushing your fish around.
one that sits in the water. Check every day to make sure the heater is working properly. The heater can break in different ways -- it could stop coming on and leave the water too cold. It can also get stuck on and make the water too hot. It could make the temperature fluctuate as if no heater is there. The thermometer lets you monitor and make sure it's working right.
A high quality food will help you fish stay healthy and live longer. Most people here recommend New Live Spectrum small fish formula pellets or Omega One betta buffet pellets. You can also get some frozen bloodworms or shrimp (not freeze dried) as treats. My bettas also like the live wingless fruit flies in the reptile area.
Prime is highly recommended by most of the forum users. It detoxifies chlorine, ammonia, heavy metals, and it does so without harming your nitrogen cycle.
I recommend one with the bulb that helps you start the siphon. Make sure you get the small if your tank is 10 gallons or smaller. You'll be using it every week to vacuum poop out during your water change.
You'll want something that tests for ammonia, nitrite, nitrate, ph, gh at the minimum. They're pricey, but the first thing you do if your fish is sick is test these things and see if there's a problem with his tank water.
Quarantine tank for medication
Sometimes, your fish may become ill. Some medicines could mess up your tank, so you want a little container ready. A 1 gallon container, even a tupperware, that hasn't had soap or chemicals on it will do.
this is what your filter does for your tank. It's not necessary, but it lets you do fewer and smaller water changes. Live plants help, too.
water change recommendations. Once you become more familiar with your tank and the test kit readings, you can tweek the water changes and do them when needed instead of at a set day.
this has a list of common diseases and the medicines used to treat them. You can stock a few of these medicines for emergencies. I have aquarium salt and seachem paraguard ready at all times.
Sorry that is so long-winded! Someone else will mention if I forgot something.