The approach I have taken with the guidance of my teacher is:
First, a little background in logic. Dignaga's Pramanasamuccaya, etc.. and then Dharmakirti. ( haven't quite completed this)
Then, studying Chandrakirti's 6th chp. of the Madhyamakavatara...drawing upon
all the commentaries and modern resources I can find. While pursuing this I have been instructed to become familiar with
the five Madhyamaka lines of reasoning and then to search for the stanzas that are representative of these lines of argumentation within the
text. The Diamond slivers and dependent arising arguments dominate and are primary to the sixth chapter of the Madhyamakavatara, but the other three are there if you dig.
All five lines of argumentation are, in some respects, interconnected and a basic understanding of them all is invaluable to study of any Madhyamaka texts.
I also found the following very helpful:
DKR's teaching/commentary on the Madhyamakavatara (already mentioned by Huseng)
Jeffery Hopkin's Meditation on Emptiness
Ju Mipham-mkhas ‘jug
And many others...