Some streaming programs are incompatible with the Live Gamer HD (it helps others out).
You have some pretty beefy specs, so I'd suggest beginning to stream/record BEFORE buying additional hardware. Then, after you've started streaming/recording, you can decided if additional hardware will even help (and can look into whether your preferred software can even use Live Gamer HD).
& whether you'll even take an FPS hit at all depends in large part on what game you'll be streaming. Some, with relatively low CPU requirements, are going to perform basically the same regardless of if you're streaming or not. Others, like SC2, are going to take a hit. Of course, they're not going to be getting anywhere near 120fps late game anyway.
Edit: currently one of the more popular streaming programs is OBS (Open Broadcaster Software), both because of its relatively small hit on system resources and because it doesn't cost money.
Here's a guide on OBS from teamliquid.net:
http://www.teamliquid.net/forum/viewmessage.php?topic_id=372629Edited by MisterFred - 6/14/13 at 4:58pm