Apartment in Berlin for 2, Near Schleiermacherstraße

As you are only coming in March (I assume you meant 2020, not 2019), there is no point looking for accommodation now. You can only search and find something once you are here!
Thus arrange temporary accommodation (at one of the websites you already mentioned - yes they are expensive, but it is only for a limited time!) until you find a permanent place.
Keep in mind that the minimum termination notice for rental flats is 3 months and most places are advertised and quickly taken right after such notice is given. Thus even once you find a place to rent, it might still be many weeks until you can move in. But you will need that time to select and buy furniture and household goods - there are very few furnished options in Germany (and those are also expensive)!