I'd recommend going to http://pcpartpicker.com/. Be sure to research heavily, too. Building a computer isn't just something you do overnight first time and get right with little to no research. You will be spending good money on this thing even if it is only 600 dollars, so please make the best of what you are getting. Do not skimp or gloss over the power supply, either. Too low of a wattage you can get from one and you could end up with a roasting computer.
http://pcpartpicker.com/p/8rCXRB
Notice how even the power supply was given a large amount of thought? Also, please be careful with what brands you are getting. Make sure the brand has a good reputation. It doesn't have to be renowned, but please be aware some brands have gotten less good as time goes on and some just aren't as good as they once were. It may be tedious to do so much research, but even a 600 dollar computer is a meaty investment and should be treated with care even during the planning stage.
http://www.build-gaming-computers.com/computer-power-supply.html
I'd say 500W is good enough if you are just doing the typical gaming, but if you are wanting heavier gaming, please go above that. At least something in the 700W range will be best for higher end stuff.
2 gigs of ram is not enough at all. RAM isn't ultra expensive, so please have at least 4 gigs. 8 gigs would be best for a gaming PC as a just in case measure if you want to make sure you get a steady stream of random memory going through those things. Mods might make those 8 gigs a requirement, too.
Please read about the precautions to take when building a computer.
My build isn't the final one, most likely. I am still planning and wondering if mine is still relevant enough to keep up with the current gen. Mine was first planned with last gen in mind, but then the PS4 and Xbox One came out.
Your motherboard is where all the action goes as far as compatibility is concerned. Please be aware of that. PC Part Picker, luckily, has a compatibility setting where you can only choose parts that will be compatible. Please use that.