The real question to ask is why you make it a series of papers rather than just one paper. If you see a clear logical separation between parts and each part is devoted to something different and/or intended for a different audience, then the division is justified and the choice of the journal should be made independently for each part (independent variables do not need to be pairwise distinct, of course). In all other cases, you should really think of why you split the way you do and tell that reason. I doubt it is possible to give a good advice without knowing the answer to this question.
Another general suggestion is to put them all on ArXiV and do full cross-referencing so that the readers of part 3 will be able to find part 1 if needed. If you just submit different parts of the series to different journals, it is possible that part 3 will appear a year before part 1 or, even worse, that part 3 will be published and part 1 will be rejected, which would result in quite a mess from the reader's perspective.