At that price point, it's crucial to decide what the PC will be used for; for gaming, more should be spent on the graphics card. If you intend to run programs that are CPU and memory intensive, such as Photoshop or audio/video conversion, you'll want a faster CPU and more RAM. Being that there are a huge number of choices involved even in a $600 build, if you want any meaningful replies, you'll have to elaborate on the intended use of the machine. Also, $600 will not get you a powerhouse no matter what the intended use, so it's doubly important to make all your choices carefully and look for sales once you decide on your path.
Early on you must also decide whether to go with Intel or AMD, as many subsequent choices depend on this. For gamers on a budget, AMD is usually the best choice. For those requiring more computing power or faster memory, Intel CPUs are the way to go.
I could make a comprehensive list for you (after you provide some more info), but then other users may give you an equally valid list that's completely different than mine. In the end, it takes a certain amount of research on your part
(reading reviews, articles, and user reviews on NewEgg, TigerDirect, Amazon, etc.) before you'll be comfortable making the purchases. Take your time and enjoy the process, because when it's done it's sort of a letdown; you're ready to build another one! But also each build is something to be proud of (if it works!), and all the more so if you hand-picked all the parts yourself.