BDAG? Yes. Personally, I find this works best with a tagged GNT that can go to the BDAG definition by clicking on a word -- this in a software package (I use Accordance, but other Bible Software packages have the same feature, I imagine); I personally think that Louw & Nida is worth having also: it may not have been the compilers' intent, but what they have produced is an excellent resource for exploring words that are closely related in meaning and differentiating them from each other in much the same manner as a good thesaurus will do for English words.
LSJ -- the unabridged -- is valuable and ordinarily worth checking even when you use BDAG, fortunately the unabridged edition is on line at Perseus Philologic at UChicago.
Smyth's grammar is a sine qua non. Although I own a dog-eared hard copy that I've had for more than 50 years, I find myself regularly consulting it online at the Perseus Philogic site at UChicago. It's useful for all ancient Greek, including Hellenistic Koine and Homer.
BDF is useful, but more useful to those who have studied some Classical Attic than to those who have studied only the Koine. I don't know of an online digital BDF other than in the Logos package, but it too is easier to use in a digital edition.
A.T. Robertson: at some point one ought to start working through the big grammar of ATR. It's now available in a digital edition in most Bible software packages and also in formats prepared by none other than Louis Sorenson.
I haven't put up the URLs for these items, but they can surely be located quickly via internet search.
ABOVE ALL: I'll cite George Somsel's admonition and repeat it ad nauseam: READ, READ, READ! Read (Greek, that is) early, read late, read when you have leisure, read Homer, read the Classical authors, read the Apostolic Fathers. For God's sake! This language you've begun to acquire is the medium of a vast amount of the best writing ever put by pen to paper by human hands. Explore it's heights and depths and breadth. Read it with the boundless interest and curiosity of an Odysseus ready to be sidetracked by fascinating new things every time his ship touched on a new shore.
Still accessible for those interested is a web page that I prepared over a decade ago -- before I retired from active teaching; some of the links may be dead but the suggested books can probably be located. It's entitled, "Reading to Extend and Keep Alive Greek Skills":
http://www.artsci.wustl.edu/~cwconrad/moregrk.html
Carl W. Conrad
Department of Classics, Washington University (Retired)