As to your first question, BDAG will not work with the Septuagint, as there are many, many words in the LXX that will not be found there. BDAG is very good for the Apostolic Fathers, and, of course, for the NT, but outside of that, you will need another lexicon.
I would recommend you get the LSJ MIddle. It has all the words in the GNT, in Homer, and will cover most of the Septuagint. If you are going to read widely in Greek, you need something inclusive and yet easy to thumb through.
As to your second question, you are looking for Greek which is easy, close to the NT and good. These three factors tend to cancel each other out. To deal with this very problem, I devised something called the GRONT scale. You can read about it herehttp://www.vnoel.com/component/option,c ... emid,1068/
I am writing in Ancient Greek not because I know Greek well, but because I hope that it will improve my fluency in reading. I got the idea for this from Adrianus over on the Latin forum here at Textkit.