What would be the best compatible 512 MB GPU(with shader 3 or 4) working with P4I45GV 3.00 /P4 2.4 GHZ/1 Gb ram ?

Http://www.asrock.com/MB/overview.asp?Model=P4i45GV%20R5.0

Any of them Shubham.

If we are to discern by a few known statements;

1) It is believed in some 'geek communities', that using the same manufacturer of motherboard chipset, and graphics chipset; to be a good thing.

For example an AMD motherboard chipset 'plays well' with an AMD ATI graphics chipset;

Nvidia motherboard chipset 'plays well' with Nvidia graphics chipset.

Intel motherboard chipset with Intel graphics..............no wait,....... there is no Intel graphics chipset, unless it is -> Integrated Graphics.
[ Intel GMA ]

(Integrated Graphics is also said as OnBoard graphics. ON the motherBOARD)

2) DOES NOT MATTER what graphics memory type is used.

Motherboard can use DDR Sdram ram memory, and graphics card can use GDDR5.

Why?
Because the graphics card has it's own Processor, and Ram Memory.

Graphics Processing Unit, or GPU; is the Processor,

http://en.wikipedia.org/wiki/GPU

Graphics memory is the ram memory.

Operates independent of the system resources.
Processor, and Ram Memory.

The graphics expansion slot on the P4I45GV (P4 i 45GV), is an AGP slot.
Accelerated Graphics Port,

http://en.wikipedia.org/wiki/AGP

It will use an AGP 4X, or AGP 8X graphics card.
Use an AGP 8X.

http://www.tigerdirect.com/applications/SearchTools/search.asp?keywords=agp+graphics+card+512mb

REMEMBER;

1) ALWAYS follow Anti-Static Precautions.

2) INSTALL the software for the graphics card F-I-R-S-T,
(Drivers and 'control panel')

THEN unplug the computer from power, follow Anti-Static Precautions, and Physically plug the graphics card into the motherboard, and install.

3) L@@k at the system requirements (Minimum) for the graphics card.
Specifically the Power Supply requirements. You need a Power Supply with enough Wattage, to handle the graphics card.

[ Handles the graphics card, and -> Motherboard, Processor, Ram Memory, and peripherals; Internal and External.
{Harddrive/s, optical drive/s; Internal
Mouse, Keyboard, external harddrive, etc; External ]

For additional questions please post in a Comment.
Regards,
joecoolvette