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I want to listen to some that are maybe less known...
I'm not sure how the question (Favorite Mozart Concerto?) relates to your listening to some that "are maybe less known." Why not listen to all of them, or the ones you don't already know; they are undoubtedly all on YouTube.
For most people - although not all, surely - the favorites are among the better known ones. I certainly couldn't list a favorite because in so many cases the favorite would be the one I am listening to at a given moment. Each one for me is a gem with its own particular colour, brilliance or depth and among them there is a great range of emotion expressed. The second movement of the Clarinet Concerto (KV622) is particularly moving but it, of course, is well-known and among the great masterworks for the instrument.
The Mozart concertos are one of the glories of music ... I think the only one that is not a masterpiece to my ears is K451 (and number 26) , which starts off with an exhilarating opening but then somehow undermines the effect with a second subject that feels out of place. But Ks 271, 413, 414, 415, 449, 450, 453, 456, 459, 466, 467, 482, 488, 491, 503 and 595 ... that is 16 masterpiece concertos, each of which I would happily sacrifice all of Rachmaninov's rather than lose. It is a personal thing but K491 and 595 are the ones I love most. The best Mozart pianist to my taste is Annie Fischer, although she only played 6 of them I think...
I'm particularly partial to the concertos described by Wolfie thus:
These concertos [Nos. 11, 12, and 13] are a happy medium between what is too easy and too difficult; they are very brilliant, pleasing to the ear, and natural, without being vapid. There are passages here and there from which the connoisseurs alone can derive satisfaction; but these passages are written in such a way that the less learned cannot fail to be pleased, though without knowing why.... The golden mean of truth in all things is no longer either known or appreciated. In order to win applause one must write stuff which is so inane that a coachman could sing it, or so unintelligible that it pleases precisely because no sensible man can understand it.
For instance, in the slow movement of K413, there is a kind of ambiguous happy/sad innocence coupled with simple lyricism that Mozart was to develop even further in his last opuses (e.g. Die ZauberflÃ¶te, K595, Clarinet Concerto):