Tank: 5 gallons in an absolute minimum, I personally recommend 10 gallons.

Water conditioner: Fish must have conditioned, dechlorinated water! Seachem Prime is the best water conditioner there is. It helps bind and negate the effects of ammonia for a time period as well.

Filter: Bettas need a filter! For a good, cheap choice, I recommend the Top Fin Silentstream 10. This will fit both 5 and 10 gallon tanks. Here is a link. This is what is called a hang-on back (HOB) filter. Other good HOB filters are the Fluval Aquaclear or Aqueon Quietflow. I prefer HOBs, but many people will recommend sponge filters. This is because HOBs can have a strong outflow current, which can make it difficult to swim for long-finned bettas. Google how to set up a sponge filter if you're more interested in those.

Baffle: If you choose to go with a HOB filter, odds are you're going to need a baffle. This is an object placed in the outflow to help cut down the current. It can be a lot of different things. For the Top Fin Silentstream 10, I use a piece of dense filter sponge cut to size, specifically this brand. Just cut a square out of it and plop it in the outflow. You will also need an intake sponge for a HOB to protect the betta's fins. This can also help cut down the outflow. The Fluval Edge Pre-filter Sponge fits the Top Fin Silentstream 10 perfectly.

Filter Media: For HOB or internal filters, you need filter media! The carbon cartridge that these filters come with are only good for removing medicines in the water as they are not permanent. Replacing cartridges destroys your bio cycle (more on that in a minute). Instead, use the Fluval Aquaclear Sponges. Polishing pads aren't required but can make your water clearer!

Heater: Bettas need a heater! Adjustable heaters are much better than pre-set heaters because you get to control the temp. Bettas need a temp of 78-82. I keep my tank on 80. This is the best there is in my opinion. 50 watts is good for both 5 and 10 gallons. Grab a thermometer too!

Decor: Make sure to get a hide cave! Bettas like to lounge around in secure, sheltered places. Make sure whatever decor you get doesn't have any sharp edges that could snag a fin, and also make sure it doesn't have small holes a betta could potentially get stuck in. If you find an ornament you really like but it has small holes, you can get some aquarium sealant to seal those holes up.

Plants: Silk or live only! Plastic plants are harmful to a betta's fins. I've had both fake and live plants, and I have to say a 100% recommend live plants over fake. They keep the water cleaner, help cut down on nitrates, and my betta loves sitting and swimming through them. You can get rooted plants that go in the substrate, or you can even get plants that don't required to be planted at all! These are call rhizome plants. Java ferns and Anubias are my absolute favorites. They can tied to decor, left free floating, or my personal favorite, superglued! I use this. Whatever glue you use, just make sure it is pure cyanoacrylate and it is gel. Let it dry before putting back in the tank. If you want rooted plants, either place root tabs in your substrate or get a nutrient-rich substrate. A good, cheap fertilizer is Aqueon Aquarium Plant Food.

Substrate: Gravel, sand, or nutrient rich substrate all work great!

Cycle: Since you already have your boy, you'll have to do a fish-in cycle. Read up on the full process in the wiki, but it ultimately boils down to regular parameter testing and water changes. Get the API Liquid Test Kit as well as some Seachem Stability to kick-start your cycle.

Food: Always use pellets, never flakes. Fluval Bug Bites, Northfin Betta Bits, and New Life Spectrum are all good foods. Supplement with frozen brine shrimp and blood worms about once a week.

Water Changes: up to 50% of the tank water once a week. Use a gravel vac to make the process easier!

Meds to have on hand: Seachem StressGuard and ParaGuard, API General Cure, Prazi-Pro, Seachem Kanaplex, Focus, and Metroplex. Read up on some common ailments for bettas.

This is an awesome starter kit (just toss the heater, in my experience it's not a very good one): https://www.petsmart.com/fish/starter-kits/top-fin-essentials-aquarium-starter-kit-5262267.html