I am aware that there are one or two questions in this vein but I am looking for specific advice pertaining to my situation.
I have completed Rudin's Functional Analysis and I'm interested in going in the Operator Theory- C* Algebras direction. Dunford & Schwartz seems like one of the only possible sequels as far as books go. However D&S is huge and I'm hoping for some advice from workers in Operator Theory & C* Algebras as to which parts of D&S are most pertinent and which papers I can start reading.
Of course, if possible I would love to start reading papers but I'm wondering if it might be a bit premature and a combination of papers and monograph might be better. Thanks.
If you're looking for a book to learn the basic theory of operator theory and $C^*$-algebras, flip those around and start reading "$C^*$-algebras and Operator Theory" by Gerard Murphy.
Additionally, one can read the latter chapters of Conway's "A Course in Functional Analysis" for another soft introduction. If you're a bit of a masochist, you can begin with Davidson's "$C^*$-Algebras by Example", though I'd personally recommend holding off on this book until you are familiar with the basics.
I would (again, personally) recommend holding off on reading papers until you are familiar with the basic aspects of operator algebras (functional calculi, approximate units, GNS/representation theory, etc). These tools are often used/cited without proof, and without understanding them, it's easy to get lost.