Is there an inexpensive modern printer that will work with a computer that runs only MS DOS (6.22)?

you will not find one. Just too old. maybe if you look at a Salvantion Army thrift store, but still you most likely are SOL. You would do better to buy a new computer at Salvation Army and then you can get a real printer for about $10 and less then $100 for a computer at the same place, thrift store