When Peter arrives at the house of Cornelius, we find Cornelius bowing down to worship Peter, quite possibly out of gratefulness to God for sending Peter to him. Peter tells him not to bow to him for he is only a man just like Cornelius. This tells me that Peter cannot be considered the first Pope for two reasons: First, he was a married man. Secondly, Peter says that he is only a man and not to be worshipped. This is in stark contrast to the view that the Pope has such authority that all those who follow him would hold him up and worship him instead of worship Christ alone.
Peter learned his lesson well from his vision of the great sheet, that he was not to call any man unclean. So when the men came to him, he was ready to immediately go with them and meet Cornelius. According to the rest of our verses it is evident that Cornelius was a worshipper of God and gave alms. I believe we are seeing the transfer from the Old Covenant v to the New gospel of salvation through Christ in this passage. God had already appointed Saul (now known as Paul) as the apostle to the Gentiles in chapter 9:15-16. What do I take away from this passage? There should be no presuming as to whether I think someone will or won't be receptive to the gospel message. I am responsible to get the message out that Christ died for all and that no one is unworthy of God's salvation.