Beside grammar, how much vocabulary do I have to know? Should I buy some latin dictionary like Oxford Latin Dictionary? Or is there any word-correction for novice learner?
As far as the base 50% vocab, a standard textbook like Wheelock will get you there. I agree with Colin that you should skip the OLD. That's more useful for prose/poetry composition. Instead, rely on Geoffrey Steadman's free online Ceasar and Cicero, and you won't need a dictionary at all. Steadman's free Caesar, Cicero pdfs for intermediate readers
You may also like the interlinear translations by Bolchazy-Carducci, but as a Latin teacher, I think those are too cluttered for an intermediate reader.
You definitely do not need the OLD, which costs several hundred dollars, and while wonderful, would be incredibly cumbersome to your reading. A copy of Cassell's will do fine. You can also download a copy of Lewis & Shorts Latin Dictionary from the Google Playstore, it's free, and pretty gosh darn good. At least to start with Cicero, I'd recommend a classroom reader of the 1st Catilinarian, there are numerous editions available with grammar and vocabulary help on each page.
As far as prerequisites, if you've finished any standard textbook, like Wheelock's for example, you shouldn't have any issues. Cicero tends to use a lot of subordinate clauses and show off with his Latin. Which while impressive, can be quite the struggle for new Latinists. Caesar is a lot more plodding and methodical, detailing his campaigns.