Who should we worship: God, the Father, or Jesus Christ?

Since both are God, that is they, along with the Holy Spirit, make up the Godhead, they are both worshiped.

"Oh come, let us worship and bow down; Let us kneel before the LORD our Maker" (Psalm 95:6).

"Then those who were in the boat came and worshiped Him, saying, "Truly You are the Son of God"" (Matthew 14:33).

"God is Spirit, and those who worship Him must worship in spirit and truth" (John 4:24).

"But when He again brings the firstborn into the world, He says: "Let all the angels of God worship Him"" (Hebrews 1:6).

"The twenty-four elders fall down before Him who sits on the throne and worship Him who lives forever and ever, and cast their crowns before the throne, saying: "You are worthy, O Lord, to receive glory and honor and power; for You created all things, and by Your will they exist and were created."" (Revelation 4:10-11).

See also:

Questions and Answers regarding Worship
Questions and Answers regarding God
Questions and Answers regarding Jesus