Hebrew resources that I own and use:
A Reader's Hebrew Bible by Brown and Smith : This is probably the best student edition of the TNK. It glosses all words which occur less than 100 times in the scripture, making it possible to navigate the texts with limited working vocabulary. However, even the "known" words can be hard to recognize (esp. weak verbs) or have different meanings in different binyanim, so keep doing the regular study along with it...
Biblical Hebrew, 2nd ed by Kittel et al. : One of the better "inductive" texts for learning BH. Some Amazon reviews seem to derail this book for lack of grammatical thoroughness, but I don't find it to be the problem at all. The teaching order may be a bit strange (beginning with wayyiqtol) but it's no less rigorous with the grammar. Keys can be downloaded and they're very helpful, though I did feel stuck very often with this book, despite the authors' attempts to make it as painless as it could be. Essentially, this book was my passport to Hebrew.
Learn Biblical Hebrew by Dobson : Another "inductive" text for BH. Unlike Kittel, this one might seem pretty shallow with grammar, especially its treatment of binyanim and weak verbs. However, Dobson focuses more on the semantics than morphology of each binyan, providing good close-ups for many common verbs in each binyan. He's also very detailed on idioms and prepositions, with a lot of example sentences from the text itself.
A Practical Grammar of Classical Hebrew by Weingreen : Unfortunately, the real Hebrew doesn't always follow the neat textbook grammar, and variations abound. Maybe it shouldn't be your first Hebrew book, but you will eventually want it. Weingreen presents all binyanim in regular forms first before tackling weak verbs, unlike Lambdin.
Introduction to Biblical Hebrew by Lambdin : This motherlover is
required to understand the phonological processes which govern the entire BH grammar. You face a rather dense section on phonology and orthography before you even get to Lesson 1, so maybe it's not wise to start BH with this, but do get it and do read it. Lambdin's details really help you understand what's going on behind the scene. He tackles weak verbs in Qal before moving into derived stems, unlike Weingreen.
A Textbook of Israeli Hebrew by Rosen : I'm really torn with this. As far as I know, this is the only textbook which teaches both BH and MH, beginning with MH and highlighting the differences between the two. Also, Rosen has more "substance" than other beginner textbooks: the first conversational passage goes on for a full page and a half, in smal prints. But Rosen's grammatical explanations are extremely idiosyncratic, and he defies the conventional terminologies: e.g. Perfect, Imperfect and Participle are called Remotive, Potential and Aorist, respectively. Traditional binyanim are replaced with "strong" (Qal, Nipal) and "Weak" (Weak I Piel/Pual, Weak II Hitpael, Weak III Hiphil/Hophal). I see that Rosen wanted to redefine "Israeli Hebrew" with a totally different analytical framework, and I sometimes love it, sometimes hate it.
I learned mostly with Kittel, with additions from Dobson, and I make frequent trips to Lambdin and Weingreen for more details, and I'm trying to work my way through Rosen and the Reader's Bible itself. I've read quite a bit of TNK in the mean time (maybe a few dozen chapters), and I think I understand anywhere from 60 to 90 percent of narrative sections. Poetry is still beyond my reach, and the wisdom literature sometimes confuse me. That's my level of Hebrew, so you don't trust my words too much..