I would suggest to just start with the necessities. You can add other items later, esp if you need to watch your expenditures. Your betta will definitely feel better once warmed and into a bigger space. I haven't had experience with the heater in your picture. I started out with a little betta kit and then expanded to a heated 5 gallon a couple of years ago. It is amazing how much a betta will perk up when he is warm and has clean water and some space.
Right now I got three female betta in a heated, planted tank