IMO your best option with that budget is check out whatever sources in your area sell used PC's, do a search for "gaming PC", and see what comes up, and then come back here with that. For 600$ you will be able to get a gaming PC capable of AH in it's current form no prob much more easily than building one for that. Example - in my area I've seen 3570k systems with 660ti or 7950 types of vid cards go for 5 to 600 dollars, complete with all the other stuff like a decent MB, HD, PSU, and such. But, to try and build something that performs similarly with newer components with a hard deck of 600 will be tough IMO. Consider that just a lower end MB and CPU and RAM alone new will be at the very, very least 1/2 of your budget, you'll begin to see what I mean I think. You'll still have a case, PSU, hard drive, optical drive, cpu cooler/fan, operating system (100$ OEM usually, 1/6 the budget). Also, if you don't have a monitor, figure an absolute minimum of 100$ for one, and that's a very low estimate. Again, I just think you would be better served with a 2 ish year old mid to mid/high level gaming system as described above.
I guess another option is to find some of the budget home systems that are out there in the 4 to 5 hundred range, and try and find one you can pop a 150$ or so video card into. That would get you in close to the 600 hard deck, with all new (albeit the cheapest of the cheap) components. Newegg currently has some combo systems in the 4 to 5 hundred range that are very basic entry level gaming systems, that with an inexpensive LCD would get you in at 600, but you may not be able to play max detail in AH's current form, much less the new version. This sort of thing, but again, no operating system or LCD monitor (figure min 200$ for this). You'll get what I mean I think when I say 600 will get you in with the very, very minimum with new equipment if you want to play AH, and that's not at max detail I would say almost as a certainty. http://www.newegg.com/Product/ComboBundleDetails.aspx?ItemList=Combo.1594758 . Again, a good used system from the last couple of years would smoke this system in performance in a big way.
IMO the video card is the focus if you're looking to play AH or any other game for that matter right now, as most of the CPUs in the last few years will be able to handle AH certainly.
This said, I'm sure that if you checked around all the various component sales sites like newegg and the like, you might be able to find enough new stuff on sale in various forms and combinations to get in at 600$ with a vid card that is at least capable enough to play AH at decent detail levels currently. It'll take some work though IMO.
Here is an example of a USED system local to me, which is an area likely much smaller with less selection available to you in the USA. It's 600$ USD, and a good example of a system that will blow away a budget new system like the newegg example.
http://www.kijiji.ca/v-desktop-computers/edmonton/gaming-pc-runs-any-game/1022555119?enableSearchNavigationFlag=truehttp://www.kijiji.ca/v-desktop-computers/calgary/gaming-pc-i5-processor-7970-gpu-10-gb-of-ram-watch-share-p/1022637402?enableSearchNavigationFlag=true
