To cycle you will need a filter and decide if you want to cycle with or without the Betta, live plants or not and if yes, then the proper lights are needed, if on city water you will need a good dechlorinator, Betta are jumpers so some type of cover, I don't use covers but I have two sets of lights over my tanks for all the plants. You will need a heater unless you live in a tropical region, some type of substrate if you plan to use it, thermometer to monitor the temp...I am sure I have missed something....lol
If you are going to cycle fishless you will need some way to test the water daily for ammonia, nitrite, nitrate, pH and an ammonia source to feed the bacteria
If you are going to cycle with the Betta and this can safely be done with proper water changes, a water test kit is a good idea but not needed per se, but I do recommended them with either method, knowing the water pram will help you decide when and how much water to change during the cycling process fish-in, otherwise you just make 50% water changes every other to every 3rd day for 4-8 weeks in a 10g tank with one Betta, again you have to have a filter to cycle with either method.
One more thing your need-water change bucket, plastic cup, net and siphon-I would label the bucket "fish only" and keep all fish related items in it for easier use.