No, it will be pretty good for the old games you are listing like starcraft, homeworld, CS:S, HL2, maybe Modern Warfare 1 at lower settings.
For a card that is capable for the others you want at least an HD4670. That motherboard does have a PCIE x16 slot right?
Well, what are the specifications of your power supply? I recommended the HD4670 as it is cheap and low power and any non-terrible PSU should handle it. If you have a capable PSU and are going to spend that much you might as well get this for $130 as it is a much better card; http://www.newegg.com/Product/Product.aspx?Item=N82E168...
What is the native resolution of your monitor? What cards you should be considering is highly dependent on resolution.
i have an AOC flat panel...i do know its 19" or bigger. But since im not at home i cant give you specific part numbers. I remember that i have at 350 power supply (round about). One hard drive (sata) one DVD burner (sata) and a video card is all that is in the machine.
Yeah, with a 350w PSU you will want to stick with the HD4670. You could replace the PSU but honestly that computer is old and the processor is pretty weak by today's standards. If you are going to start replacing multiple components you should just build a new system entirely.