I'd go with the mini. The one I have has a shorter lower base. The sponge almost sits on the bottom. This gives a longer lift tube for more flow. You can adjust the flow with a $3 valve in the airline.
Yeah, that's good stuff. As much as will fit in your filter. A 3x3 in square of 1/2in thick floss is plenty of area for one Betta. You might have to clean it more often than sponge. Keep an eye on it and let me know, please.