So far I still haven't finished Part II of his Functional Analysis because I have not that much motivation to study more of differential equations, but other than that let me put down what I can think about about this trilogy, which may answers your question, partially.

* A hidden motivation of all three books should be, explaining his *Fourier Analysis on Groups*. After studying some parts of first two books you should be able to give this book a try.

* It is not necessary and not realistic to read all three books linearly. For example, the prerequisite of R&C is PMA's first 7 or 8 chapters. R&C's final chapters are somewhat technical and you may want to read them when absolutely needed. By the way chapter 18, on Banach Algebra, is a lightweight version of the Chapter 10 in his Functional Analysis (you may simply skip it if you will go into part 3 of Functional Analysis; a lot of duplication). For his Functional Analysis, he arranged a map of logic chains. If you see it, you will realise that after first 4 chapters (and chapter 5 for some specific examples) you can jump to part 2 or part 3 as you wish, because these two parts are not that related. Trying to do everything linearly will burn yourself down real quick.

* As I am studying number theory, I'm really grateful about Rudin's setting in his books. In his R&C he put everything into "locally compact Hausdorff space" whenever possible, meanwhile from what I've learnt, many objects in number theory may enjoy this property. As a result I have less things to worry about whatsoever.

* Rudin did not teach you how to compute things, but he did not think it was not necessary. Instead, he thought you could handle them yourself. Therefore you may need some extra help.

* Exercises. Some exercises are classic (counter) examples, some ask you to fill the gap in main text, some are asking you to prove other key theorems, some are fairly technical things, asking you to reproduce theorems proved by other mathematicians (maybe from a 1909 German paper and it's nowhere to be found on the Internet). I think first three are really important.

* When I was studying chapter 6 of R&C, I felt lost because I had no idea why this should be that. But when I was studying chapter 11 or 12 of Functional Analysis those in R&C came up naturally and everything connected. I suppose many have to go through this kind of journey.

* If you don't have motivation to study complex analysis anyway, at the very least you should finish chapter 10 of R&C. This is the so-called bread and butter.