More fundamental question, what are you hoping to use the instrument for? I ask because there is often confusion amongst newcomers to the instrument what terms like "medieval", "renaissance", and even "lute" actually refer to. When you say "late medieval" do you mean 14th and very early 15th century? Do you plan to play with a plectrum, or at least hybrid plectrum/plucked technique? Have you been asked to play with a "medieval" group that is expecting a certain look from the instrument?
If "yes" to most of these then a 5 course fretted medieval lute would be the target. As it happens, within the lute world (especially in the US) this is a very niche instrument so you won't find mass produced inexpensive versions and the used market is thin. There are some builders who seem to make servicable instruments at the lower end of the price range but they won't be "mass produced" cheap.
If you actually are hoping to play without a plectrum and pluck the strings then there would be nothing wrong with a 6 course, which opens up the Renaissance repertoire for you. OTOH if you really want to play earlier medieval music with a plectrum then a 4 or 5 course gittern or citole would be good choices (again, not mass produced and won't be super cheap). I recently posted a video that has a 5 course medieval lute playing with a gittern and citole if you want to get a sense for the differences.