The MX440 would be a good choice, it's basically a high end Geforce2 and it's one of the more common and cheaper cards. Make sure it has 128-bit memory though (most do but some deceptive ones don't).
But if you find a good price on a Ti4200 then I see no reason not to use that instead, unless you just have some sentiments about what card "feels" right with what you want to build.
The Ti4200 would generally be overpowered for a P3-600, but that just means you have headroom for future upgrades without the video card being a limitation. It also means you can run higher resolutions without a framerate drop.
If your friend stays interested in the hobby, he might end up with more motherboards and CPUs in the future, and the Ti4200 can come in handy with those also.
The Ti4200 is likely to increase in price more than an MX card ever will, so if he's in the market for a video card and finds a good price on a Ti4200, it's a good investment to get it now instead of later.
The only downsides I can see with the Ti4200 are higher power consumption and maybe less reliability, but those are unlikely to be a problem. Just make sure the pegs that hold the heatsink in place are in good condition and that the fan isn't dying.
If they are close in price then I'd say the Ti4200 is great, but don't spend a lot for it. On a P3-600 you probably won't see much difference from a fast Geforce2 to an MX440 to a Geforce3 to a Ti4200 but the difference will grow at higher resolutions. I don't have benchmark figures but I would expect you'll see a difference at 1600x1200, maybe at 1280x1024. If your friend does have a 1600x1200 monitor, keep in mind that using 800x600 mode is an option, and at that res all these cards would perform about the same.