Paul recommends the 10” (25cm) with 16-19 PPI. There are many different names on the saw plate but only one chief maker. They usually come in 6, 8 and 10” sizes, however the 10” will do everything the smaller sizes will do. You shouldn’t have to pay more than £20.
Paul recommends new where possible for this saw as a secondhand one will probably need restoration, reshaping of teeth and sharpening. As these are smaller toothed saws, they are more problematic to sharpen which might not be ideal for a beginner.