Perhaps one of these? The one that's for 5-15 Gallon tanks looks like it would plug right into the built-in tube in the tank.
Filter: any sponge filter rated for 5-10g should be sufficient. You need an air pump, air line tubing and check valve for it.
Example: https://www.amazon.com/Hygger-Aquarium-Single-Sponges-Submersible/dp/B07XZ625DG/
https://www.amazon.com/UPETTOOLS-Aquarium-Biochemical-Sponge-Filter/dp/B08JGQ1ML5/
Air pump kit example (attach to sponge filter instead of air stone): https://www.amazon.com/FEDOUR-Aquarium-Oxygen-Bubbler-Gallon/dp/B0BVLH4MKG/
Also!!! PLEASE DON’T RUSH TO GET THE BETTA! A new aquarium and new filter needs 2 weeks-1 month or so to cycle, for beneficial bacteria to get properly established. https://injaf.org/articles-guides/beginners-guides/the-nitrogen-cycle-and-the-fishless-cycle-getting-your-aquarium-ready-for-fish/
Get Seachem Stability if you want to help speed things along (and double/triple the dosage as you like - more beneficial bacteria added will help speed the nitrogen cycle more, and any extra will balance out and die down eventually).