I'm running Xubuntu 64bit on a similar system with a Core i7 2600, an SSD, and a Radeon HD 6870 with an Asus P8P67 motherboard...I haven't had any problems with it running Linux so I don't see why it wouldn't work for you. It's been suggested in the past by the folks at Canonical that you only run the 64bit version if it's not a production box (I'm not sure if they still say that), but I've been running a 64bit version of Ubuntu since 10.04 and it's worked just fine.
Generally speaking Radeon HD cards have better support in Linux than NVIDIA cards, so you're doing fine there. But you've also got a pretty good beast of a machine so it shouldn't have any problem with handling Unity in Ubuntu 12.10.
The only thing that I would be concerned with is how small your SSD is...I have a 120GB SSD and my root partition is running low on disk space continually...so you might consider getting another hard drive to handle your /home directory and give the root partition more than 8GB of space (which I believe is the default amount of space Ubuntu gives to the root partition).
Aside from that - you can run Ubuntu from a live cd and try out all your hardware to make sure that it works before you install it. Installing drivers in Ubuntu is pretty simple...there's a section in the preferences/settings that says "additional drivers" where the drivers for your video card, wi-fi, etc. are kept and you can choose to activate them or deactivate them at will. In some cases it can get more complicated than that, but there are plenty of people at the Ubuntu forums who are more than happy to help you out (provided you've adequately searched the forums/Internet to make sure you're not asking a question that's already been answered).
Also, make sure that you select to install the additional plug-ins during install (I forget the exact wording) - it's a little check box at the bottom of the screen during the setup before you start installing the OS...without those plug-ins you won't be able to listen to MP3s or watch many types of movie files. It's also a good idea to make sure that you have your machine connected to the Internet during the install so that you don't have to install a bunch of updates after you finish installing.
Good luck!
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