Before I spend 850$ on my first build, could someone reassure me that this is a good investment?
Will this computer be able to run fraps while playing combat arms and call of duty?
Here's some benches with the 5770. Although the test system might be a lot better than the setup you're looking at, it shouldn't matter TOO much as the GPU is what you should rely on when it comes to gaming.
If you need build either post here or start a new thread. I recommend reading through my step-by-step guide in my sig, read your MOBO manual & shortstuff_mt's sticky and you should have no issues with your build.