The best card you can safely run on a 250 Watt PSU is the Radeon HD 5570. It is a DX11 card, so it can also do DX10, it's more powerful than any of the 6600 series nvidia cards, though it's not exactly a powerful card by today's standards. However, most cards more powerful than the 5570 would probably be bottlenecked by your CPU. Edit: I might be wary of running a 5570 on that 250 Watt, capacitor aging has probably reduced that old PSU's capabilities, you may need a new PSU either way.
Your motherboard should not care how large a power supply you have. The only recommendations I see in mobo manuals are the minimum PSU you should have for a system, and usually they recommend a 300 Watt to be on the safe side, even if you are only using...