You didn’t specify Deck or Engine so I’ll suggest what worked for me (and if you look around, you can find a lot of these things online free of charge in pdf form)
Modern Marine Engineer’s Manual vol 1 and 2.
Pounder’s Marine Diesels
US Navy rate training manuals: Engineman, Machinist’s Mate, Electrician’s Mate, Damage Controlman, and the NEETS (electronics) modules. Also get Fluid Power for a good primer on hydraulics
NSTM (Naval Ships Technical Manuals) are good, too. Here’s a list http://www.fas.org/man/dod-101/sys/ship/nstm/001v0r42.pdf
The reason why I like the Navy training manuals is that they start out very basic and are written for people with average aptitude and intelligence. Plus, the USCG uses them frequently for exam questions.
The NMC actually publishes a reference list on their website which I recommend you have a look at. You don’t need to purchase all of the books obviously, but you will get a good idea of what to look for.
Engine reference library: http://www.uscg.mil/nmc/training/exams/pdfs/engineering_exam_reference_library.pdf
Deck reference library http://www.uscg.mil/nmc/training/exams/pdfs/deck_ref_library.pdf
Lastly, be familiar with the CFRs or at the very least, how to use them (each exam room has copies)