i learned the alphabet from the book "teach yourself ancient greek", which teaches attic-dialect and not koine, but still works for learning the alphabet. i only used it because it was sitting on the shelf at the library and so was easily accessed.
the alphabet is extremely easy, you could set one day aside for it and afterwards have it.
for the greek text of the new testament i'm still using the NA27 because i have a hardcopy of it with me, and don't feel up to dropping the money on the NA28 at the moment. i use the christogenea new testament because it's literal and unbiased. for the old testament, i'm using rahlfs septuagint (altho i don't have a hardcopy yet).
for the l&s, the version i posted was just so others would have access to one and it was what i found first. i'm unaware of later versions being politicized, but since you've brought it up i'll look into it. based on the quote you provided, tho, it certainly seems that way.
regarding the greek enchiridion, i contacted Hendrickson Publishers, and they said that the rights have gone back to William G. MacDonald since the book is out of print, but they have no idea how to contact him personally and i've been unable to find a way as well, so for the moment scanning a copy of it and uploading it here won't work. but it's available for really cheap, as low as $3 plus shipping, so that shouldn't be a hurdle.
to understand for yourself, i'd suggest, before anything else, familiarizing yourself with all of the grammatical terms and ideas on the tyancientgreek site, such that you know them by heart.
learn the alphabet and reconstructed pronunciation if you seek to be able to speak the language and have it sound really musical, or just a basic pronunciation if you just seek to read it.
then learn a lot of the most common words, which the wikipage is very helpful with. the pronunciationguide i posted was from a man who teaches a certain reconstructed pronunciation that seems good, and sounds nice to my ears.
i myself am only using the lexicons of l&s and lust for now.
this is how i'm learning it at the moment. i haven't taken any classes or anything on it, and am glad that i haven't done so because most of them are in error because of their tradition.
anyway, hope this helps. feel free to ask any questions you want.
also, if you haven't purchased any hardcopies of either the greek old testament or new testament, check out:
http://www.scholarly-bibles.com/product ... raeca.html