你的句子有问题.应该是：There is such a variety of mobile phones that we don't know WHICH to choose.因为已经指明了范围（a variety of mobile phones ）,所以不能用what.如果用how,就必须是：There is such a variety of mobile phones that we don't know how to choose ONE(==a mobile phone ).在你的句子里,choose是及物动词,后面必须加个宾语.
好,已经搞定了.研究和比较一下吧.