No level of GPU is "needed" for Photoshop. If you are not planning to do any gaming, integrated should work just fine. Instead, use the money you save to pick up some extra RAM, the fastest processor you can afford, and ensure that you have sufficient HDD space. In the world of photoshop, any of these components are more important than the video card.
Out of the graphics solutions you have mentioned, the 8400M GS is the only dedicated option. Low end dedicated cards are great because they can help avoid the usage of system memory for Vista Aero and provide significantly better performance. Also the GF 8M series can accelerate video playback. On the other hand, since you have voiced no intention to do any gaming, this card is far from necessary. If your budget is tight, use the money on any of the things mentioned above.
The other three GPUs are all inegrated. The 945GM is the weakest. I'm not entirely sure how the X3100 compares to the 6150- in games I believe the 6150 ends up being faster, and seems to have better support ATM... however, the X3100 has excellent potential and may end up surprising us all with future driver updates. Any of these should serve you fine if you only want to do Photoshop + Aero or even very light gaming; however, the 945GM should be avoided in favor of the other two solutions.
Best of luck on your next purchase.