"He thinks a lot."
Translation:Он много думает.
I entered both очень and много into a context search-engine at reverso.net. It returned a lot of Russian phrases and sentences which indicated that очень is a kind of intensifier adverb which you'd used to translate "very", while много was used to translate "much" and "a lot of".
If these are any indication, then you'd choose много over очень for the same reason you'd choose "much" over "very" - "He thinks much" vs. "He thinks very".
I'm almost getting used to the word-order preferences. My natural inclination now is to put adverbs in front of verbs, and also words like здесь. It's at least become my first choice, and I seem to get things right a lot more often by doing so. I just don't quite know why - not yet, at least.