People hear the word "baptism" and immediately they add the word "water" in their minds. "Baptism" in today's world has become synonymous with "water baptism". And in Jewish society people would have thought the same thing, since water baptism originated as a Jewish custom.

However, John the Baptist who was in the Old Testament (see Luke 16:16), knew that Jesus was coming to bring a different understanding of baptism, just as he was going to do with so many of the old traditions and laws. Jesus' baptism was going to maintain the spirit of the old baptism, but without the outward religious ritual.

This is what John the Baptist said of Jesus:

"There comes one mightier than I am, after me, the latchet of whose shoes I am not worthy to stoop down and unloose. I indeed have baptized you with water; but he shall baptize you with the Holy Ghost." (Mark 1:7-8, Matthew 3:11 and Luke 3:16)

Here is the man who was most famous for baptising people with water, saying that Jesus' baptism would be a different baptism. And we know that Jesus did not baptise with water himself. (See John 4:2.) So Jesus lived up to what John the Baptist had said of him, in that Jesus' baptism was a spiritual one, and not a physical one.

"Go therefore and teach all nations, baptizing them [with the Holy Spirit] in the name of the Father, and of the Son, and of the Holy Ghost, teaching them to observe all things whatsoever I have commanded you." (Matthew 28:19-20).

Certainly water baptism does not feature heavily (if at all) anywhere else in what Jesus taught.
But when you understand that the baptism Jesus was referring to was a baptism of the Holy Spirit, then the sentence makes much more sense... especially when you understand, that the teachings of Jesus are God's Spirit. (See John 6:63.)
The instruction to teach people to observe what Jesus commanded, is not only clarifying what to teach, but it is also clarifying how to baptise people!
When we present people with the teachings of Jesus, we are in effect presenting them (or 'covering' them) with the Holy Spirit. If they choose to accept (or 'drink in' which is what 'believe' means) the truth in His teachings, then they are being filled with the Holy Spirit. John 6:63 says that Jesus' words are Spirit and life. That is how we understand this command and that is what we take seriously.

... Jesus allowed his followers to baptise with water even though he himself didn't. (John 4:2) In itself there is nothing wrong with the practice (of baptising people with water). It is a symbolic thing that hopefully represents something that is happening spiritually within a person.

But there is nothing in the Bible to indicate that water baptism is essential for Christians. Baptism, on the other hand, is essential; but remember which baptism is Jesus' baptism (the one with the Holy Spirit).

So yes, it is essential to have the Holy Spirit (i.e. to be 'baptised' or 'covered' with the Holy Spirit) to be a Christian, but it is not essential to be water baptised. (Romans 8:9)