In the fish-in cycling the Ammonia comes from the fish's waste, so you don't need to add any to the tank. But you will need the chemicals to dechlorinate the water during the many many water changes that you will have to make to ensure your Betta's gills don't get burned from the Ammonia.
You will definitely need the Ammonia test kit to test daily at least once for the levels of Ammonia in your tank. Aim to get it as close to 0 as you can. Anything above .25 is harmful for the fish, even at .25 for prolonged periods of time there can be organ damage to your fish.
Once you see the Ammonia levels not rising quite as high or even disappearing you will have a build up of the first beneficial bacteria in your filter. They eat the Ammonia and convert it into Nitrite. But Nitrite is also toxic for the fish, and that is when you will need the Nitrite test kit. Again you will need to aim to get the levels as close to 0 with frequent water changes.
Where a low pH may be beneficial during the Ammonia stage, because it makes the Ammonia less toxic, a low pH makes the Nitrite stage more toxic. That's why it is good to know where your pH sits so you are prepared!
When the Nitrite is getting lower or disappears then you are almost there. Then you will see the Nitrate rise and these are normal in a tank, but at very high levels those too are toxic! That is one of the reasons we do weekly water changes in our aquarium, to keep the Nitrate levels somewhere between 5 and 20. There are however others who believe you can aim even a little higher than that.
Weekly water changes replenishes also other things in the water we can not test for, or are more complicated to test for!
Another thing you may want to find out at some point is how your water stands in regards to hardness, to dissolved minerals in it. That will be very important to know if you are going to add snails or shrimp to your tank since they need those minerals to build their shells!