All of this playing around on the LAN is OK, but you really want to do some serious Internet testing. Do you need a special ISP, or can you do it yourself?
You do need a special service provider. You have two options: an ISP that offers native IPv6 networking, which would be wonderful, or a broker that offers a 6to4 tunnel, which uses special routing that encapsulates IPv6 traffic inside of IPv4. ISPs and brokers give you a block of IPv6 addresses, just like a native IPv6 provider, and also offer DNS services. You may connect a single host, or set up a gateway for your LAN. 6to4 tunneling is transitional, and will eventually disappear in favor of native IPv6 networks. Here is a list of tunnel brokers, and doubtless a web search will find more:
Hexago.com (http://www.hexago.com)
SixXs.net (https://noc.sixxs.net/)
Hurricane Electric (http://www.tunnelbroker.net/)
BT Exact (https://tb.ipv6.btexact.com/start.html)
AARNet IPv6 Migration Broker (http://broker.aarnet.net.au/)
Each provider offers different tools for managing your service, so you'll need to follow their instructions for getting connected. Most of these offer free services, and it's a great way to get experience managing an IPv6 network.
Deepspace6 (http://www.deepspace6.net/) is a good resource for Linux IPv6 admins