John, the baptist???

Matt. 3:1   Now in those days John the Baptist came, preaching in the wilderness of Judea, saying,  2 “Repent, for the kingdom of heaven 1is at hand.”  3 For this is the one referred to by Isaiah the prophet when he said,

“THE VOICE OF ONE CRYING IN THE WILDERNESS,

‘MAKE READY THE WAY OF THE LORD,

MAKE HIS PATHS STRAIGHT!’”

4 Now John himself had a garment of camel’s hair and a leather belt around his waist; and his food was locusts and wild honey.  5 Then Jerusalem was going out to him, and all Judea and all the district around the Jordan;  6 and they were being baptized by him in the Jordan River, as they confessed their sins.

What kind of baptist was John?

John was a levite priest. He was the son of Zacharias. He was born to this world 6 months prior to Christ. He was Jesus’ cousin. The scriptures do not elaborate on what John actually did in the temple as a Levite.
We can ascertain from the book of Hebrews that John did perform one ritual:

Heb. 9:6   Now when these things have been so prepared, the priests are continually entering the outer tabernacle performing the divine worship,  7 but into the second, only the high priest enters once a year, not without taking blood, which he offers for himself and for the sins of the people committed in ignorance.  8 The Holy Spirit is signifying this, that the way into the holy place has not yet been disclosed while the outer tabernacle is still standing,  9 which is a symbol for the present time. Accordingly both gifts and sacrifices are offered which cannot make the worshiper perfect in conscience,  10 since they relate only to food and drink and various washings, regulations for the 1body imposed until a time of reformation.

‘Various washings’. This word in the Greek is rendered as ‘baptism’.

909. βαπτισμός baptismos; from 907; (the act of) a dipping  or washing: —washing(1), washings(2).

This is essentially the same word used to describe the baptism that went on in Acts, chapter 2:

Acts 2:41 So then, those who had received his word were baptized; and that day there were added about three thousand souls.

Was this baptism that was occurring under Peter’s preaching at the Pentecost event the same type of baptism that John was calling people to? Not entirely. Similar, but not one and the same.
John’s baptism was a baptism of repentance; it was different in that Christ had not yet died and officially, it was not the new sign, yet. As well, the question to ask, even in light of all the most prominent commentators agreeing that John’s baptism was a Christian baptism, is, did John baptize in the commissional formula of the Trinity? If not, can it be a Christian baptism?

John Lightfoot says it was not Trinitarian:

 

III. The baptism of proselytes was an obligation to perform the law; that of John was an obligation to repentance. For although proselytical baptism admitted of some ends,—and circumcision of others,—yet a traditional and erroneous doctrine at that time had joined this to both, that the proselyte covenanted in both, and obliged himself to perform the law; to which that of the apostle relates, Gal. 5:3, “I testify again to every man that is circumcised, that he is a debtor to do the whole law.”

But the baptism of John was a ‘baptism of repentance;’ Mark 1:4: which being undertaken, they who were baptized professed to renounce their own legal righteousness; and, on the contrary, acknowledged themselves to be obliged to repentance and faith in the Messias to come. How much the Pharisaical doctrine of justification differed from the evangelical, so much the obligation undertaken in the baptism of proselytes differed from the obligation undertaken in the baptism of John: which obligation also holds amongst Christians to the end of the world.

IV. That the baptism of John was by plunging the body (after the same manner as the washing of unclean persons, and the baptism of proselytes was), seems to appear from those things which are related of him; namely, that he “baptized in Jordan;” that he baptized “in Ænon, because there was much water there;” and that Christ, being baptized, “came up out of the water:” to which that seems to be parallel, Acts 8:38, “Philip and the eunuch went down into the water,” &c. Some complain, that this rite is not retained in the Christian church, as though it something derogated from the truth of baptism; or as though it were to be called an innovation, when the sprinkling of water is used instead of plunging. This is no place to dispute of these things. Let us return these three things only for a present answer:—

1. That the notion of washing in John’s baptism differs from ours, in that be baptized none who were not brought over from one religion, and that an irreligious one too,—into another, and that a true one. But there is no place for this among us who are born Christians: the condition, therefore, being varied, the rite is not only lawfully, but deservedly, varied also. Our baptism argues defilement, indeed, and uncleanness; and demonstrates this doctrinally,—that we, being polluted, have need of washing: but this is to be understood of our natural and sinful stain, to be washed away by the blood of Christ and the grace of God: with which stain, indeed, they were defiled who were baptized by John. But to denote this washing by a sacramental sign, the sprinkling of water is as sufficient as the dipping into water,—when, in truth, this argues washing and purification as well as that. But those who were baptized by John were blemished with another stain, and that an outward one, and after a manner visible; that is, a polluted religion,—namely, Judaism, or heathenism; from which, if, according to the custom of the nation, they passed by a deeper and severer washing,—they neither underwent it without reason; nor with any reason may it be laid upon us, whose condition is different from theirs.

2. Since dipping was a rite used only in the Jewish nation and proper to it, it were something hard, if all nations should be subjected under it; but especially, when it is neither necessarily to be esteemed of the essence of baptism, and is moreover so harsh and dangerous, that, in regard of these things, it scarcely gave place to circumcision. We read that some, leavened with Judaism to the highest degree, yet wished that dipping in purification might be taken away, because it was accompanied with so much severity. “In the days of R. Joshua Ben Levi, some endeavoured to abolish this dipping, for the sake of the women of Galilee; because, by reason of the cold, they became barren. R. Joshua Ben Levi said unto them, Do ye go about to take away that which hedges in Israel from transgression?” Surely it is hard to lay this yoke upon the neck of all nations, which seemed too rough to the Jews themselves, and not to be borne by them, men too much given to such kind of severer rites. And if it be demanded of them who went about to take away that dipping, Would you have no purification at all by water? it is probable that they would have allowed of the sprinkling of water, which is less harsh, and not less agreeable to the thing itself.

3. The following ages, with good reason, and by divine prescript, administered a baptism differing in a greater matter from the baptism of John; and therefore it was less to differ in a less matter. The application of water was necessarily of the essence of baptism; but the application of it in this or that manner speaks but a circumstance: the adding also of the word was of the nature of a sacrament; but the changing of the word into this or that form, would you not call this a circumstance also? And yet we read the form of baptism so changed, that you may observe it to have been threefold in the history of the New Testament.

Secondly, In reference to the form of John’s baptism [which thing we have propounded to consider in the second place], it is not at all to be doubted but he baptized “in the name of the Messias now ready to come:” and it may be gathered from his words, and from his story. As yet he knew not that Jesus of Nazareth was the Messias: which he confesseth himself, John 1:31: yet he knew well enough, that the Messias was coming; therefore, he baptized those that came to him in his name, instructing them in the doctrine of the gospel, concerning faith in the Messias, and repentance; that they might be the readier to receive the Messias when he should manifest himself. Consider well Mal. 3:1, Luke 1:17, John 1:7, 31, &c. The apostles, baptizing the Jews, baptized them “in the name of Jesus;” because Jesus of Nazareth had now been revealed for the Messias; and that they did, when it had been before commanded them by Christ, “Baptize all nations in the name of the Father, and of the Son, and of the Holy Ghost.” So you must understand that which is spoken, John 3:23, 4:2, concerning the disciples of Christ baptizing; namely, that they baptized in ‘the name of Jesus,’ that thence it might be known that Jesus of Nazareth was the Messias, in the name of whom, suddenly to come, John had baptized. That of St. Peter is plain, Acts 2:38; “Be baptized, every one of you, in the name of Jesus Christ:” and that, Acts 8:16, “They were baptized in the name of Jesus.”

But the apostles baptized the Gentiles, according to the precept of our Lord, “In the name of the Father, and of the Son, and of the Holy Ghost,” Matt, 28:19

John Lightfoot, A Commentary on the New Testament from the Talmud and Hebraica, Matthew-1 Corinthians, Matthew-Mark, vol. 2 (Bellingham, WA: Logos Bible Software, 2010), 63–66.