The benefit of Gelfand and Fomin is that everything is rigorous. It is presented clearly, and there's really very little uncertainty in what they are saying. You'll read the first 100 pages and know all you need to know about the Calculus of Variations. It is a lovely book.
I read Lanczos a few...
If you're self-studying real analysis, make sure you check out the videos of Francis Su's course at Harvey Mudd College. He's a wonderful teacher, and his course covers the first 5 chapters of Rudin.
Personally, I'm not a huge fan of these intermediate books. I found real analysis on the line...
This remains one of my favourite math texts. It gives you the language of sets and relations, functions and cartesian products, equivalence classes and 'the axiom of choice', plus a little more advanced set theory, in an easily digested format. You'll also understand Russell's paradox in a new...