Not to discourage you from building your own computer, but most people just don't have the temperament or desire to do what's necessary to build their own computer. It definitely requires much more time and effort on your part to do all the research required to select the components for building a good system at a low cost, than to buy a complete computer system.

Unless you're willing to make that commitment, your question is moot.

There are definite advantages to building your own computer, if you are willing to invest the time to do it properly. I have built all my computers for years and can't imagine ever buying a complete system again. But I don't recommend others do the same unless they have a real interest in doing so.

All anyone can do is tell you what's right for them, not what's right for you. The very fact you've asked this question suggests that you have never built a computer before. The actual process of building a computer is not that hard, but the process of choosing which components to buy is where most of the work lies, especially if you don't know what the issues are. If you are still considering it, I suggest shopping around a bit to get an idea of what's available at what prices and what the issues are. If you find yourself completely lost and bewildered, then buy a complete system. But if you enjoy reading about the different components and view the process as an interesting challenge, then building your own computer might be for you.

Here's a thread about this very topic and with some advice.

And, there's always plan B: if your principle goal is just to have smooth playback during editing, then perhaps you should keep your current computer and look into transcoding your AVCHD video sources to some other format that requires less horsepower to work with. There are others here that have taken that approach and could give advice about that.