Trying to uderstannd wireless N...Can it run alongside a/b/g?

I know cureent wireless networks can do a/b/g mixed signals for different computers. My dad and Sis who i live with have a netbook and notebook that accept a/b/g signals. If I get a new router with wireless N capability can it do a/b/g/n all at the same time while I set it up for me with a new wireless N network?

 

You've overcomplicated things a bit and seems you've made your requirements towards the new router higher than they really are.
Your father and sister have computers that can use a/b/g but this doesn't mean they will use them simultaneously. So assuming they stick with 802.11g you can go for 802.11n on your notebook and all you need is a single band 2.4GHz 802.11n router.
Keep in mind that when you use both 802.11g and 802.11n on one band (2.4GHz) 802.11n packets are "dressed up" as 802.11g for compatibility reasons- so you lose some throughput for 802.11n.
If you Wi-Fi card supports 802.11n for 5GHz band you can go for a simultaneous dual band router- and run two separate SSIDs. One network running in 802.11g on 2.4GHz band for your family and another one on 802.11n 5GHz for you. That way you could achieve full 802.11n throughput.

There's another question though- do you really need 802.11n speeds? Because it's the only reason to go for it- if you really do a lot of LAN transfers from a computer that's wired to the router.