Well, I took a little Hebrew in college. Here's the thing:
1) The NT is the source of most doctrine, because the OT doesn't concern itself with that. We can see some concepts, but it's mostly by bathing oneself in the literature, and that's tougher to do.
2) Another complication is that Hebrew (like other Semitic languages) is an extremely odd language to westerners. They thought completely differently from even the people of Jesus' time. For instance, there is really no time element in Hebrew. Either something's completed, or it's not. This means that present and future tenses don't really exist in Hebrew - although they could use the type of verb that meant "incomplete action" to distinguish it from "completed action" which often (but not always!) is translated as past tense in English.
3) Being such an ancient language, and parts of the OT contain some pretty archaic Hebrew for which we have very little outside examples (the Ugarit find has been slightly helpful), we don't know much about the intricacies of Hebrew, or even how to translate many words or phrases. Take an NIV and look at how many footnotes say, "Or, [blank]," or even "The meaning of the Hebrew for this phrase/word is uncertain" (e.g., 2 Samuel 13:18-19). In such cases, the translators often go to the Septuagint, which was a late translation into Greek (around 250-100 B.C.). In fact, the quotations of the OT we find in the NT are most often from the Septuagint.
This is not to discourage you, but to set realistic expectations. I would love to learn more Hebrew, but it's tough. I agree that if we knew more it would help, but you won't likely be able to "open up the scriptures" the way we can almost do with Greek and the NT. But it is pretty awesome to read, considering how old it is, and considering that these are the very words of the OT prophets!