If your aim is to understand modern Chomskian syntax, in the sense of work produced between the original presentation of the 'minimalist programme' in 1992 and Chomsky's latest published technical work on the matter, dated about ten years ago, McCawley's book (or C.L. Baker's, or A. Akmajian's, or N. Smith's, all of which you refer to) will not help you at all. They are all excellent textbooks on syntax and on the early development of TGG, but appeared long before the minimalist programme was conceived (and positively 'destroyed' much of the theoretical basis of previous transformational generative grammar).
I would recommend you to, instead, read, first, Andrew Radford's Syntactic theory and the structure of English (Cambridge UP, 1997) and the same author's Minimalist Syntax. Exploring the structure of English (Cambridge UP, 2004), two excellent and detail-rich textbooks (with glossary and exercises), then a very different earlier book by Juan Uriagereka, Rhyme and Reason. An Introduction to Minimalist Syntax (MIT Press, 1998), which offers a comprehensive account of both the minimalist philosophy in the context of general science and most of its technical apparatus at the time, then, Howard Lasnik's Minimalist Analysis (Blackwell, 1999), Norbert Hornstein's Move. A Minimalist Theory of Construal (Blackwell, 2001), Liliane Haegeman's Thinking Syntactically. A Guide to argumentation and analysis (Blackwell Publishing, 2006), and, in no particular order, Howard Lasnik & Cedric Boeckx's A Course in Minimalist Syntax (Blackwell Publishing, 2005), Cedric Boeck's Understanding Minimalist Syntax (Blackwell Publishing 2008), and, to gain a wider perspective on 'biolinguistics' - apart from Uriagereka's already cited early Rhyme and Reason - Massimo Piatelli-Palmarini, J. Uriagereka & P. Salaburu's Of Minds and Language. A Dialogue with Noam Chomsky and Chomsky's recent video lectures on YouTube. At that stage, you could perhaps go 'backwards' and read Chomsky's own technical papers in The Minimalist Program (MIT Press, 1995, especially chapter 4), his papers on semantics and the philosophy of language in New Horizons in the Study of Language and Mind (Cambridge UP, 2000), and his last major technical papers, 'Minimalist Inquiries. The Framework' (MIT Occasional Papers in Linguistics 15, 1998), 'Derivation by phase' (MIT Occasional Papers in Linguistics, 18, 1999), 'Beyond explanatory adequacy' (MIT Occasional Papers in Linguistics, 20, 2001),'Three factors in language design' (Linguistic Inquiry 56.1 (2005):1-22) and his paper 'On Phases' (initially 2005). [All the latter papers - except the LI one - preliminarily published in MITOPL, have since been republished as book chapters in later compilations, but, as far as I can tell, with no significant revision, so it's not worth your while to spend two hundred dollars or so to buy the 'definitive' versions].
Reading just that will give you a sound technical basis to tackle the thousands of broadly minimalist papers and monographs that have appeared in the last two and a half decades. As far as I know, no major theoretical breakthrough has occurred in 'minimalist syntax' since about 2008. On the contrary - as I extensively argued elsewhere - with the adoption of 'just-recursion' and 'no tampering' as the core principles of the Language Faculty (as now understood), Chomsky's 'minimalist programme' has virtually reduced his initially ambitious and interesting view of the Human Language Faculty to near emptiness. The 'real action' from about 2008 onwards has been taking place, to my knowledge, in cognitive psychology, psycholinguistics, neurolinguistics, brain science,..., but not really in Linguistics, something you should perhaps consider very carefully if you are about to start an academic career as a linguist.
