I'd like to upgrade my graphics card to play newer games.

PC is:

Sony vaio pcv-rz32G
pentium 4 cpu 2.60g hz, 2.59 ghz,
512 of ram
Windows XP home

Graphics card is:

NVIDIA GeForce4 MX 440 with AGP8X (Sony)
PNP Device ID PCI\VEN_10DE&DEV_0181&SUBSYS_A0101043&REV_A2\4&38B71F77&0&0008
Adapter Type GeForce4 MX 440 with AGP8X, NVIDIA compatible
Adapter Description NVIDIA GeForce4 MX 440 with AGP8X (Sony)
Adapter RAM 64.00 MB (67,108,864 bytes)
Installed Drivers nv4_disp.dll
Driver Version 6.14.01.4303

And what about my power supply? Will I need to upgrade it as well?

In all honesty you really need a newer rig.
The CPU is under powered and you are seriously lacking RAM.

In all honesty you really need a newer rig.
The CPU is under powered and you are seriously lacking RAM.

Really?
Total Physical Memory 512.00 MB
Available Physical Memory 159.34 MB
Total Virtual Memory 2.00 GB
Available Virtual Memory 1.93 GB
Page File Space 1.24 GB
Adapter RAM 64.00 MB

How much would you say I need?

As a MINIMUM 1 Gig.
Put it this way I'm currently running 6 Gb on Windows 7 x64.
It really depends on what you are thinking of doing with it.
This set up will be fine for everyday 'net use, but awful as a games machine.

Also, I shouldn't say newer games. I mean games like City Life, the later Sims games etc. requirements: 3D graphics card with 64MB RAM and T & L (transition and lighting)
As far as the memory, maybe I could just fill in the empy slots to take it to 1GB
Slot 'DIMM0' has 256 MB
Slot 'DIMM1' is Empty
Slot 'DIMM2' has 256 MB
Slot 'DIMM3' is Empty

Can you recommend a 3D card with 64MB T & L?

Fill it with 512 Mb's or even 1 Gb sticks, assuming you can find them for the right price.

As for cards, you need to make sure to get an APG card and not the new PCI-e as it won't fit.

Have a look on eBay.

Thanks, I'm considering
PNY GeForce 6200 Graphics Card - 350 MHz Core - 512 MB DDR2 SDRAM - AGP

For less than $50 (25 or so pounds)

Certainly an improvement over your current card.