The apostles were tasked with selecting someone to replace Judas, who had betrayed Jesus and subsequently hanged himself. In their selection process we gain an insight into the reason for the selection: the need to have another witness among the people.
And this reason gives us an insight into the focus of their witnessing.
Therefore, of these men who have accompanied us all the time that the Lord Jesus went in and out among us, beginning from the baptism of John to that day when He was taken up from us, one of these must become a witness with us of His resurrection. Acts 1:21-22
The apostles were not focused on the fact that Jesus was a great teacher, or that following Him meant a better lifestyle, or that He was a pretty nice guy. They were witnessing to the fact that Jesus is God, that He had risen from the dead, and that He had walked among them, alive, and ascended miraculously back into Heaven.
To them, the truth that Jesus is God the Savior was an overarching, all encompassing, wonderful, powerful truth.
May our witnessing have the same focus.