Hm. It's not really necessary, the books stand alone enough that you can read any book in the series without having read the rest - I did, started with Babel Tower. But if you're intending to read all four, obviously reading them in order would probably be better. Not so much for spoilers - I didn't think my knowing some things beforehand ruined my appreciation of the second book - but because that way the evolution of Frederica's character and those of some other characters will make more sense. It's a bit confusing if you read out of order as I'm doing. And I suppose reading a book while waiting all the time for certain things to happen, because you've read the sequel, does change the way you read things. If you know from the start that something that seems to be going well will end in drama, or conversely that something apparently heading for drama will end well, it probably doesn't impact you the same way when the change occurs.

Well, the focus is more on Tennyson's friend for whom he wrote that early mourning poem than on himself, but still.