I am also a non-native speaker... my method to read those old English text is to first read a summary or outline (in modern English) of the original work, and

I am also a non-native speaker... my method to read those old English text is to first read a summary or outline (in modern English) of the original work, and then perhaps find some more modern English material on the subject to deepen my understanding...but eventually, I would try to read the original work, as the melody (they call meters; but I feel it is essentially isomorphic to rhythm in music) and the rhyme in those works written by Shakespeare, John Donne, or John Milton (as well as many other great writers) are really really superb, and not that different than the corresponding parts in literary works in other languages. Reading a summary and outline would help you to gain some contextual information, and then you could use some redundancy in human language to get better the intended message the writer hopes to convey...