Is it orthodox to abandon the concept that God of the Bible is person, but say that He is spirit? Should I abandon the concept that God of the Bible is person, but say that He is spirit? 

I would mean that God the Father, God the son and God the spirit are persons, but God means different qualities in the Bible that make it one essence. So God would not be person like eg. Son of God is, but rather a spirit being. God is of one essence, but exists in three "persons". That is what I meant when I asked that whether to interpret God as person or as a spirit. I meant that God the Father, Son of God, God the spirit are defined as persons, but God defined as spirit being rather than person. I mean by spirit that he is not literally made of matter, but is a spirit being like Holy Spirit is. So in this matter it seems that God of the Bible is of one essence of divinity; spirit being, and manifests in three persons, who yet are each God. So our God is of one essence, but of three persons.
I ask to answer my first question and maybe comment on the last phrase.

If I do, is this in keeping with the historical expressions of the faith?

My motive for this is to discern how the concept of God in Islam is different from the concept of God in the Bible. In other words I try to help myself to discern how the concept of God in the Bible is different from the God of Islam.
In a mainstream evangelical understanding, God's essence does not consist of anything created.  Matter is created.  God is spirit and existed as such before the creation of matter or time or space.  A "body" is something physical, and only the Second Person of the Trinity has a body, which He received at the Incarnation.

Personhood does not mandate a physical body.  Every creation is lesser than its creator.  Thus, we could not have personhood unless God first possessed Personhood.  

So, in summary, God is spirit, which is not matter, and He does exist in Three Persons, only One of which has a body, but He did not always have one, receiving His body at the Incarnation, which was later glorified at His resurrection.