I interpret your question as “what things should I concentrate on to get the biggest and fastest payoff from my studies?”.
In grammar, I’d say the little bit that will get you 80% is learning to recognize the case markers for the most common noun classes, O-stems, like θεος theos ‘god’ (masculine), and the A-stems, like βιβλια biblia ‘book’ so you can solve what the Russians call the 'KTO KOGO?" problem, i.e., know who’s doing what to whom. (The short version is that the “victim”, or direct object, likes to take an -n ending in the singular.) Your Russian will help you tremendously there, both in getting the overall system (only four cases–can you believe it?! The dative is the “garbage can” category where instrumental and locative/prepositional functions get dumped) and in many of the details. (There’s a Greek grammar tutorial in Russian with helpful declension tables, at http://www.greeklatin.narod.ru/grk1/index.htm.) For verbs, the “core” is the main present tense patterns (you’ll find that most of them fit into two big classes, an E-stem class, and an A-stem class, just like in Russian, with endings that will look very familiar to you) and the fact that the prefix e- is the past tense marker.
In vocabulary, I would approach my textbook like a phrase book and highlight the high-frequency vocabulary that I want to learn first with a yellow highlighter. For me, the most-wanted vocabulary includes the question words, the personal pronouns, the numbers, and adverbs of time and manner, etc. (as in Russian with KOGDA-TOGDA, or English ‘when’-‘then’, there’s a helpful pattern with ποτε-τοτε, etc.), names for family members, ‘day’ and ‘night’, ‘yes’ and ‘no’, verbs like ‘come’, ‘go’, ‘is’, ‘do’, ‘eat’, ‘live’, ‘die’, and so on. Even if you don’t expect to use your new vocabulary to get around in ancient (or modern) Athens, it’ll still come in handy when you try to read things in Greek (I find biblical passages easiest, where I highlights bits of simple dialogue like ?αββι, που μενεισ? ‘Rabbi, where do you live?’).
The pronunciation question is a Pandora’s box. Good (and very passionate!) arguments can be made for either a Modern Greek pronunciation or a reconstructed ancient pronunciation, and arguments can even be made for a convenient (i.e., lazy), English-like pronunciation. My advice is, whichever you choose (I’m going the Modern Greek route, myself) don’t miss the opportunity to get your ears to pitch in with the learning process along with your eyes. (Even Dobson’s heavily British-accented recording accompanying his Biblical Greek text can be very helpful in learning vocabulary and grammatical structures. It’ll certainly nail down in your head phrases like εγο γ?αφο τους λογους, ego grapho tous logous, ‘I write the words’, which can serve as a readily available example of “accusative plural” later while you’re reading something. Even moreso, learning to count or ask questions in Modern Greek from a Pimsleur tape, or the like, from your public library will similarly pay off in memory and comprehension of the numbers and interrogatives in Ancient Greek–in addition to the benefits of knowing some Modern Greek). Finally, don’t neglect the accent marks (as I have in the few Greek words I’ve typed here–simply because I haven’t learned how to type them yet!). (The argument that since we don’t know exactly how the ancient pitch accent sounded, we should ignore them, I don’t find terribly convincing.) The main pitfall for the English speaker is inconsistency in the vowels; Greek, like Spanish, but unlike English or Russian, is very “democratic” in allowing the unstressed vowels in words like “democracy” to keep their individual character.
I don’t know if this approach is “Pareto-optimal” (I’m familiar with that concept from economics, though the 80-20 rule is new to me), but I hope you find it helpful.
I wish you a trouble-free, but exciting, conquest of the 80%! I look forward to reading about your discoveries.
