Why was Christ typified by a serpent?

I read a reference about the brazen serpent that moses lifted up. It seemed at first a little odd that the Serpent would be a symbol of Jesus, because it was also a symbol of Satan.

Here are some of my thoughts:

The original serpent was Lucifer, who caused--who brought about the fall.

I think, although I'm not sure, that Brass is symbolic of things telestial… things earthly. Specifically in the temples etc. of the old testament.

So Christ takes on the physical form that Lucifer took when he brought about the fall, made of earthly material. He identified himself with (as) the sinners, and was raised up. All who look to him can be saved. Lucifer's (serpent's) curse was that he would forever go on his belly in the dust. The type of Christ was a flying serpent, able to raise itself out of the dust.

In his life the Savior took the physical appearance of the sinners. He subjected himself to the fall, and wrapped himself in an earthly flesh. He was able to raise himself from the dust, was raised up among sinners as a symbol that can lead us back to salvation.