"I hear people say that Network Address Translation (NAT, RFC 2663) will do the trick. In that case I can keep my current addresses and network infrastructure."

Is NAT cascading, or Carrier Grade NAT (CGN), an alternative for IPv6? NAT does prolong the lifetime of current IPv4 networks, but has issues with accessibility (the end-to-end principle) and scalability (the number of concurrent sessions is limited).  CGN will provide a short-term solution for ISPs who are not IPv6-ready on time. However their total amount of investments will increase, since they will have to move towards IPv6 anyway later on.