JD, I still haven't watched anything aside from the two latest movies... But I think I'd rather read the books in order to build fresh pictures in my mind - I admit I'm a little afraid of the "old" looks of the technologies and characters in the original movies and series...
I don't know that there's a correct order to the novels. Some of them are numbered, but the numbers don't accurately reflect when they happen in time. I would recommend picking out a few novels that interest you and going from there.
If you're worried about understanding the technology of TOS, it might be easier to start with something like Star Trek Constellations
. This book isn't one story but several short stories together. Each story features one or two of the characters, so you should be able to get a sense of their personalities and tendencies from them.