Our prayers should be aimed at who? I know that Jesus died for my sins, and I know that we pray in Jesus' name, but should we ask Jesus or God the Father?
The most definitive answer comes from Matthew 6:9

This, then, is how you should pray:
“‘Our Father in heaven,
hallowed be your name,

But in prayer words are for you, not for him. Matthew 6:8 says:

Do not be like them, for your Father knows what you need before you ask him.

Jesus and God the Father are aspects of the same - at the end of the day it matters little which you pray to. If Jesus' name comes more easily to you then don't feel you must 'correct' yourself.