In a nutshell: As a general rule, we use “much” (or “many” in the plural) in the negative, in questions, and when modified by an adverb. In addition, the word “many” is in general use to talk about units of measurement (time, distance etc.). For example: Not much/many. They didn’t eat much food / many hamburgers. Did they eat much food / many hamburgers? How much/many…? So/too much/many. Not much/many. They worked many hours. They walked many miles. Etc. In all other cases, we usually use a lot (of) or lots (of). Note: Native speakers can break these particular "rules" (more like "customs") with impunity, but my advice to ESL learners is that they should first get accustomed to using these rules, and only start to break them after passing a C2 test. BTW, this is a typical question with Russians in particular, so I’ve given this answer before (http://classic.italki.com/question/354092)

Несмотря на то, что much употребляется с неисчисляемыми существительными, употребление его следует не везде. Ибо иногда это будет звучать просто нереально. Твоё предложение звучит так: "Я пью неисчисляемое количество кофе". Я пью столько кофе, что даже невозможно подсчитать сколько я его выпиваю. Вообще с неисчисляемыми употребляют "a lot of". Я повсеместно с этим сталкиваюсь.

There's no such thing as too much coffee.

If you want to sound natural, B is correct. I can't really give a good reason why, though, just that... nobody really says "much" in this sort of context. A lot of means there's a large quantity. "I drink much coffee" isn't WRONG, it's just... usually it'd be more like "too much," as in, you drink an excessive amount. I think maybe much is used for less easily quantifiable amounts of things. Such as, "we feel much gratitude," or, "there's much joy in the air."

If you were speaking to the person face to face and said "I drink much coffee" you would usually do a hand gesture to indicate how much it was. So i would go with B if this is just written. I drink a lot coffee ( sounds better than i drink much coffee, if that is just all you're saying)