I absolutely live by sponge filters when it comes to bettas! I don't know any other filter that has so much control; what's better is that you can run multiple filters off one air pump! The biggest downside is the noise the pump can make if it or the cable is vibrating against anything though this is usually easy to rectify through some gentle nudging into the "right" position.
I don't have a photo of my divided tank (waiting for it to send from my phone... takes a whiiiile) but I have the heater on one side, filter on the other and they are both pressed up against the divider. My tank is somewhere between 13 and 14 gallons and is also planted.
There are two types of sponge filter you can buy: stand-alone ones (which have a weighted bottom) and stick-to-the-side ones. I like the stick to the side ones, they often have two sponges on them (depending on size) and are super efficient.
Something I'd personally suggest buying if you go for a sponge filter is a non-return valve -- especially if your air pump will be sat outside the tank below the water line. Non-return valves stop the water from being sucked into the air line and going into the air pump and therefore increase its longvity. They cost anywhere between $0.50 and $5, depends on brand you get - they are tiny
though so it might be worth getting a spare in case you need to change airline tubing and lose it!