The promise of the New Covenant is to who?

In Acts 2 we see all the wonder of Pentecost that was fortold by Joel when the Holy Spirit descends on the crowd and thousands are converted.  In the midst of all this we see Peter preaching the Gospel in verse 38, "Repent, and be baptized every one of you".  This directly followed Peter's explanation of how Jesus, who a few days ago was dead at the hands of the Jews according to Gos's sovereign plan, arose, and now sat at His Father's right hand as reigning King.  This Jesus was also now their Judge, and they saw that they stood at the mercy of the One they had crucified.  

"Now when they heard this they were cut to the heart, and said to Peter and the rest of the apostles, "Brothers, what shall we do?". To which Peter replied, "Repent and be baptized every one of you in the name of Jesus Christ for the forgiveness of your sins, and you will receive the gift of the Holy Spirit.  For the promise is for you and for your children and for all who are far off, everyone whom the Lord our God calls to himself."

Why did he mention their children?  Why would the New covenant promises apply to them?  This verse should sound familiar.  "I will establish my covenant as an everlasting covenant between me and you and your descendants after you for the generations to come, to be your God and the God of your descendants after you." -Gen 17:7. This promise directly followed the event of God blessing Abraham and making a promise to him to make for Homself a people and give them the Land.

Both of these proclamations say the same thing, that the covenant promises, Old and New, are for us and our children.  So two questions arise.  First, are circumcision and baptism related?  Second, should children receive the New Covenant sign?

More to come!