I believe the very first thing that needs to be taught is what being born of God is when one is born again. The entire scenario from being drawn of God to Jesus through the conviction and guidance of the Holy Spirit. Also the position of a believer in being born again with a corrupt and mortal flesh, and how one becomes transformed with the Word of God as opposed to being conformed to the world which is at enmity with God.
After explaining who the believer is in Christ Jesus as a born of the Spirit individual with a corrupt flesh that one is to put to death continually in order to abide in Christ Jesus walking in the flesh, the steps of maturing as a believer should be taught. I believe that 2 Peter 1:5-11 should be taught as the steps to spiritual maturity of the believer.
Add to faith (born again believing faith in Jesus Christ which is knowing the word of Him being crucified for our sins, and knowing that he resurrected to life) virtue (which is the wanting to do what is right in God's eyes). Add to virtue, knowledge (which is learning the Word of God to know what is right in God's eyes), add to knowledge, temperance (which is self-control to overcome the flesh, the world, the temptations of satan), add to temperance, patience (knowing that patience will be necessary to wait on the Lord for all things whether you fall, or plateau, or feel weary, etc.), add to patience, godliness (which is the common walk of walking in the Spirit of God imitating the mind of Christ Jesus), add to godliness, brotherly kindness (reaching this level of maturity allows a believer to love his neighbors as he loves himself), and ultimately add to brotherly kindness, charity (which is the love of God, agape love. This allows a believer to love the Lord God with all of their heart, mind, soul and all their strength.)
This is in my mind that most important teachings that one could pass on to new believers. An understanding of their faith, and how to mature in their walk with Jesus Christ.
5 And beside this, giving all diligence, add to your faith virtue; and to virtue knowledge; 6 And to knowledge temperance; and to temperance patience; and to patience godliness; 7 And to godliness brotherly kindness; and to brotherly kindness charity. 8 For if these things be in you, and abound, they make you that ye shall neither be barren nor unfruitful in the knowledge of our Lord Jesus Christ. 9 But he that lacketh these things is blind, and cannot see afar off, and hath forgotten that he was purged from his old sins. 10 Wherefore the rather, brethren, give diligence to make your calling and election sure: for if ye do these things, ye shall never fall: 11 For so an entrance shall be ministered unto you abundantly into the everlasting kingdom of our Lord and Saviour Jesus Christ. 2 Peter 1:5-11