There isnt a real difference between brands. Both are reputable companies.
What resolution is the TV? I'm sure the 4670 will run them--but maybe not at your highest resolutions. Tom's rates the 4670 as "Good 1680x1050 performance in most games"
You might consider bumping up your price range a little. Newegg has $99 4850s that are significantly more powerful.
Or you can get the new 5670 (the 4670 replacement) that has DX 11 and is faster than the 4670 for high $80s.
The tv resolution is 1920x1080, but yea I won't be playing games at that resolution. Not really sure yet what res to play at, all my life I've played with CRAPPY video cards so I'm only familiar with 800x600 or lower (I know, sad isn't it...). But due to my smog check costing more than what I had initially thought, I think I'll get the Sapphire card.
Free shipping definitely, but sadly there is tax. I can't wait for it to arrive, is there anything I should do before I install it aside from unplugging the computer? This will be my first time ever doing anything like this so I want to make sure I do it right.
You have the idea. Unplug computer and make certain to discharge any static electricity so you dont make any random shocks in the computer.
If you have an old card you might want to uninstall the drivers from it first, but if you were just using integrated graphics dont worry about it. You might be better off downloading a driver from either the ATI or sapphire website(it doesnt matter) instead of using the one they send on CD-- the online one will be newer.