$250 is the very cheapest you will be able to build a complete system.
I would recommend against getting the video card or the mobo/psu/ram/cpu, because either way you will have an extremely bottlenecked computer.
Unless of course you plan on saving up another $200 dollars relatively soon, in which case I suggest getting the mobo/ram/cpu/psu first, and getting the vid card later.
Heres my proposed build if you cant.
Foxconn A78AX Socket AM2+ 770 Motherboard - $65
AMD Athlon 4400+ Brisbane 2.3ghz - $59
Sapphire HD3650 512mb Video Card - $60
Hec 585watt PSU (Like the one you suggested but this one has a 6pin PCIe connector) - $22
My friend has had this exact PSU running an overclocked E2160, 2gb DDR2667, and an 8800gs for 4 months now with no problems, its heavy, and the build quality is superb for its price, HEC is just one of those up-and-coming brands who is trying to get their foot in the door by keeping their prices low, much like how Rosewill started out
Total: $245.04 Shipped to my address
And those not a bad computer at all, the 3650 may not be top-of-the-line but its a whole hell of a lot better than the x1300, and will run most games at medium-high. I would put it at about the same level as an X1800XT
Edit: Just saw that you said you might be able to save up $300 for this build, and if you can, get this instead of the 3650:
Its a HIS Radeon HD3850 512mb for $120 before MIR which brings your total to $305 shipped to my address.
But it has a $30 Mail in Rebate which brings your total down to 275$, which, considering what you are getting (a complete, AthlonX2/3850 build) is a damn nice price.Edited by HugeDink - 6/30/08 at 10:44pm