A 10 gallon tank is perfect. You can never keep a fish in a tank that is too big.
Since bettas don't like a lot of flow in their tanks, you have to be careful with what filter you buy. The best type of filter is a Hang-on-back filter, or HOB. It's also good to find one where you can adjust the flow. Aquaclear filters are good, especially because you can fill them with your own filter media, and not waste money on useless cartridges.
You will also need a heater for the tank. A 50 Watt heater is best. The temperature should be set to 78 degrees Fahrenheit.
You'll also need a thermometer to monitor the temperature in the tank.
The tank will also need a lid. Bettas are jumpers, so a secure lid is very important. If you buy a tank kit, it will come with a lid and a light. If you don't buy a kit, then you will have to get a lid and light separately.
The glass lids sold at petco are fine.
For lights, it depends on if you're going to grow live plants in the tank (which you really should as your betta will love them). The Nicrew lights are pretty cheap, and are very good.
You will also need an aquarium vacuum, to do your weekly water changes and vacuum the substrate.
You also need a dechlorinator to dechlorinate the water before putting it in your tank. This is not necessary if you are using well water.
For substrate, this again depends on if you want to grow plants, and what plants you want to grow. You can get a nutrient rich substrate if you want to grow plants like crypts, pearlweed, anything that takes the nutrients from the roots. If you want to grow things like anacharis, java fern, anubias, anything that takes its nutrients from the water column, you won't need nutritious substrate,
If you don't take nutritious substrate, you can get some gravel or sand from the pet store.
When you're aquascaping your tank (arranging your decorations, wood, rocks, etc.) keep in mind that bettas like things that they can hid in. They also like tight spaces. Don't put in anything so tight that your betta would get stuck, just something where he can feel nice and secure.
So, after you have set up your tank, you have to cycle it before adding a fish. You can look up how to cycle your aquarium using the fish-less cycle method.
Once your tank is cycled, you can get your fish.
Also, make sure that you get your fish a variety of good quality fish foods. Hikari, OmegaOne, New Life Spectrum, and Bug Bites are all good brands. Make sure you get the betta pellets, as bettas need a lot of protein in their diet, unlike most tropical fish species. You should also feed your fish some kind of frozen food, like bloodworms or brine shrimp.
Also, do you know the PH, KH, and GH of your water? The GH is the most important, as this will tell you how hard your water is. Bettas are soft water fish, and living in hard water will kill them.
I know this is a really long post, and I'm sure it's kind of daunting, but I want to make sure you know everything about betta care before you get your fish.