Some people throw around the word "type" pretty carelessly. If scripture doesn't actually say something is a type, I prefer not to call it one. Here in John 3 we have a case where scripture specifically calls something a type: just like Moses lifted up the serpent in the wilderness, so also must the Son of Man be lifted up (John 3:14).
We tend to worship what has been lifted up. The children of Israe eventually began to worship that serpent, until Hezekiah destroyed it (2 Kings 18:4). Hezekiah understood that the serpent was only brass, it wasn't actually what had delivered Israel.
Well, we're in a slightly different position. The Father wants us to honor the Son exactly the same way we honor the Father (John 5:23). So where Israel was wrong the worship the serpent, we are right to worship the One who was lifted up for us.
We understand that the Son of God became the Son of Man, at least in part so the He could be lifted up for us.
We worship Him because He is God (John 1:1). Hebrews 1:10–12 tells us (quoting Psalm 102) that He laid the foundation of the earth, and the heavens are the works of His hands. We worship Christ Jesus because He is the creator of all things: not one thing came into being without Him (John 1:3).
We remember Him because He gave Himself for us (Galatians 2:20). Of course we don't minimize who He is as God from eternity, but we understand that it was in a sense a much greater thing for Him to give Himself for us than it was to create us. Being made sin for us (2 Corinthians 5:21) cost Him much more than creating the heavens and the earth.
We remember that the Son became the Son of Man so that He could be lifted up for us. He gave His flesh to be food and His blood to be drink (John 6:53) so that lost sinners could have eternal life. He poured out His soul into death, and was made an offering for sin for us (Isaiah 53:10–12).
