Luke 1:3

It seemed good to me also
Being moved to it by the Holy Ghost; for he did not undertake this work of himself, merely by the motion of his own will, but was influenced, and directed to it by the Spirit of God, as well as by him assisted in it:

having had perfect understanding of all things;
relating to the subject of this Gospel, concerning the conception, birth, ministry, baptism, and death of John the Baptist; concerning the conception, birth, private and public life of Christ, together with his sufferings, death, resurrection, and ascension. The Syriac and Persic versions refer the word "all" to persons, to the eyewitnesses and ministers of the word; rendering the clause thus, "who have been studiously near to them all": and both senses may be taken in, and the meaning be, that Luke had diligently sought after, and had attained unto a perfect knowledge of all the affairs of Christ; having studiously got into the company of, and intimately conversed with all, or as many as he could, who had seen Christ in the flesh; and were, from the very first of his ministry, attendants on him, that he might have the most certain and exquisite account of things, that could be come at:

from the very first;
and to the last; from the conception of John, the forerunner of the Messiah, which is higher than any other evangelist goes, to the ascension of Christ; though some choose to render the word here used, "from above", as it may be, and sometimes is; and may signify, that the evangelist had his perfect knowledge of things by a revelation from above, by divine inspiration; and this moved him to write, and which he mentions, that Theophilus, to whom he writes, and every other reader, may depend, with certainty, on what is said in it. This clause is omitted in the Syriac, Arabic, and Persic versions, but is in all copies, and by all means to be retained: this being the case, these reasons prevailed upon him, as he says,

to write unto thee, in order, most excellent Theophilus;
which regards not so much the order of time, which he does not always strictly observe, as the particulars of things, related in order, and with great exactness: who this Theophilus was, to whom he writes his Gospel, cannot be said; by his title, which is such as was given to governors of provinces, as to Felix and Festus, ( Acts 23:26 ) ( 26:25 ) , he seems to be, or to have been, a civil magistrate in some high office; for though not many rich, and mighty, yet some have been, and are, called by grace. Theophylact