That was interesting and highlights that I do not know a whole lot about networking. What would be a good source to get a basic understanding of these things work?
The course is free and you can do it on-line. You will have to do certain tasks, (e.g. set up a ipv6 capable mail server), HE will check and if you were successful you enter the next level. If you make it through to sage level you will get a free T-shirt (which in my case they even sent for free to Germany).
The tasks are not difficult but completing the course will take some time. It is hands on experience and I learned a lot. I'm not affiliated with HE in any way.
Maybe you need a VPN to your company, or university? Unless it's some high security stuff, set up a client on the router and route the traffic through it to selected networks.
Or maybe your ISP doesn't offer IPv6 yet and you'd like to use it? Get a tunnel from SixXS[2], or HE[3].
Set up a file server, bridge your network with your parents' network, and let them use it. Keep their backups for example.
Create a completely separate open wifi network if you live in a densely populated area. You can also route its traffic through some other host, if your ISP doesn't look kindly on that sort of thing.
Learning without goals in mind seems a little tedious.
[1] http://wiki.openwrt.org/toh/netgear/wndr3800 [2] https://www.sixxs.net/main/ [3] http://www.tunnelbroker.net/