not necessarily, you need to go better PSU just because of a gfx card. and your budget is quiet high demanding for just onboard gfx.
My suggestion goes like this
MSI P45 Neo-F/MSI P43 Neo with no gfx card + 8600GT 512 MB DDR3 card. will run good with any 400W PSU,
Look on this page for gfx card prices List of GFX card with prices. and you will realize in 8-10K, you can go for good mobo + better gfx card than any onboard solution + a good PSU.
My suggestion of PSU is coolermaster 460W in 2.4K
-----------------------------------------
Posted again:
-----------------------------------------
8600GT card I suggested is from palit
another good option is sapphire HD 4350 512 MB DDR3, of which itware price is 2650.
Remeber a good PSU helps you run your system better and longer without any problem.
-----------------------------------------
Posted again:
-----------------------------------------
could not get a show of sapphire HD4550 512 MB DDR3, which is also a cheaper card.