I have debated many times as to whether to send you this reply. I have noticed that you have asked several questions regarding recommendations for study material.
Maybe I can share my personal experience with you. I don't know how extensive your background is. But I started studying math rather late in life (66 to be precise). I was somewhat fortunate in that I had always wanted to study math, and one day came across a small interview of Vaughan Jones discussing his favorite math books. I had no idea who he was at the time. But I checked out the books on Amazon and clearly they were way over my head.
However I did learn that Prof. Jones was a Fields Medal recipient (aka Noble Prize for math). So I periodically checked his website. One day I hit the jackpot. THere was a set of beautifully transcribed notes from his real analysis course.
As you may know, real analysis is quite often the foundational course in studying (let's say) real math.
So I really didn't have the problem of deciding amongst an array of otherwise good to great books.
I studied those notes day and night many times over. In essence I didn't read them, I lived them.
So on the one hand, it's important to find a book that you can deeply engage with. But likewise it is most fruitful if you can fully commit to it. That entails writing down key concepts, going through proofs inch by inch, drawing pictures. Testing yourself if you can convincingly present the material. And, the best of all worlds, if you can prove things before reading on in the text or with just catching a glimpse or two of what lies ahead.
Hopefully I have painted a good picture of what studying a math text entails for me.
I would not necessarily try to line up an array of future texts. Even though you say you read a lot; this isn't quite like reading. This goes at a pretty slow pace and if you miss a word or phrase it can produce difficulties.
Rather focus on one text - making it yours is what I would suggest. That does not mean you should not consider other reference material on the same topic. For example in addition to Vaughan Jones's notes:
https://sites.google.com/site/math104sp2011/lecture-notes
I also went through the first four chapters of Pugh's "REal Math. Analysis."
This worked very well on a complimentary basis.
In conclusion, I would most sincerely suggest that you pick your level (if possible real analysis). Pick a primary text. (Keep in mind that there are some texts that are more what I would call teacherly - where the intention is to explicitly open your eyes to the material. And some that are more "opaque" where you have to supply a lot of the details. They both have their place.)
Best of luck,
Broadly speaking, a book's age does not serve to credit or discredit it. That being said, it's a bit like asking, "Is a Magnavox Odyssey still valid"? If it still plays, then it still plays, but you also have to deal with the fact that old things are meant to do different things than new things, and that even if two things have the same goal, time will still help to refine that thing through innovation.
Will Hardy's analysis be correct? Most likely. But you run into two things, especially when you're talking early twentieth century books. For one, the language will be very unorthodox by today's standards. If you're going particularly early in this period then you might even find dissent among authors as to what to actually call what we would refer to now as a "set" (I believe Russell had used "manifold" at some point for what is now a set, and now manifold has a very particular meaning in geometry). Be prepared to Google what words mean, and be prepared for that Googling to be a nontrivial endeavor. It's also important to note that an important part of mathematics is knowing how to read and communicate it, neither of which will be possible if your lexicon is a century old.
Secondly, their methods and approaches will probably not be what we'd use today. This is the refinement. Over time, mathematicians will look for better ways to do what the older folks did. It's common that a classic theorem's proof when first presented will consist of multiple lemmas, and will be a long and drawn out labor, while later authors will "streamline" and "refine" those methods. So though what folks like Hardy might give you is in all likelihood correct, it's also likely that later authors will have improved upon what the classics present. And when I say "improvement", I don't mean that some stuffy journal has found some generalization of a theorem to the point that it's almost unrecognizable; I mean that your typical undergrad text will do in six lines what an older author did in a page and a half, and probably in a reasonable generalization.
EDIT: This newfound brevity might also sometimes be a mater of saying something very similar to what the older authors were saying, but simply having more precise language to say it with.
Best Answer
Spivak is very good for learning calculus as it has very thorough explanations (though sometimes become too chatty). Be sure to do all the exercises. Have Apostol by your side too.