The answer regarding to whom we pray to revolves around why Jesus Christ came to the earth in the first place. What is most interesting about Jesus' mission on earth was that He came to reveal the Father, not so much to play up His own credentials, as great as they were. For example, John 1:18 reads as follows.
18. No one has seen God (the Father) at any time; the only begotten Son, Who is in the bosom of the Father, He has declared Him. (John 1:18, HBFV throughout)
Similarly, verse 37 of John 5 states the following.
37. And the Father Himself, Who sent Me, has borne witness of Me. You have neither heard His voice nor seen His form at any time.
Since God in the Old Testament was seen and heard (Exodus 20:1, 30:17 - 23, 34:5 - 7, etc.), this shows that the God of the Old Testament was Jesus, not the Father.
Given this understanding of the relationship within the Godhead, that Jesus came to reveal the Father among other spiritual truths, we can then understand why He told His disciples to talk directly to the Father. The "Lord's Prayer" should not be memorized and mechanically repeated, but rather it should serve as an outline that suggests what to pray about in what general order. Notice how this outline tells us to communicate with the Father.
9. Therefore, you are to pray after this manner: 'Our Father Who is in heaven, hallowed be Your name . . . ' (Matthew 6:9)
Therefore, our prayers should normally be directed to the Father. We should pray in Jesus' name, which means by His authority. For our petitions to be effective, we should mention we are speaking in Jesus' name near to when we are ending our prayers to the Father (See John 14:14, 16:23, 26).
This is not to say it is a sin to pray to Jesus directly. We know that, given a standard interpretation of the context and translation of the words in Hebrews 1, that the angels bow down and worship Jesus (Hebrews 6:1). However, we should not make this our primary practice.
We should avoid making the mistake of exalting Jesus' role in saving us from sin and eternal death that we neglect the Father's role in our salvation. After all, Jesus' sacrifice was about reconciling us to God the Father.
10. For if, when we were enemies, we were reconciled to God through the death of His own Son, much more then, having been reconciled, we shall be saved by His life (Romans 5:10).
In conclusion, we should pray to the Father that Jesus came to reveal.