You are showing a Hang on the Back filter (HOB) which are fine for smaller tanks (like yours). The only filters that "clean" under the gravel are Under Gravel Filters (UGF), and they have some issues. You need to be very diligent in your gravel vaccing, otherwise you lose flow through the filter and they are useless after that. There are also REVERSE under gravel filters. Personally, I'm not interested in either since they don't work with sand, and my cories need sand. (They are also problematic with planted tanks as well.)
I use two Penguin 200s on my 56 U.S. gallon tank, and I'm very happy with it. The flow could be a little higher, but to be honest, I don't think it needs to be any higher. If needed a powerhead can always be added to a tank to increase circulation. And if a sponge is placed over the intake, it can be used as filter as well - just be sure to squeeze out the sponge regularly to prevent blockages.
The simplest to set up is a HOB filter - these are also fairly easy to maintain and are fairly inexpensive. The externals are best (necessary for larger tanks), but are a little trickier for a newbie to set-up, potentially messier to deal with if you don't know what you are doing with the hose connections, and far more expensive. Then there are internal filters which are very similar to the HOB filters, except that they stay IN the tank. These are best for smaller tanks. If I were you, I would go for a quality HOB filter (or two).