I haven't done any work on this front, but I think about it intermittently.
I think white lithium grease is probably a decent choice. I think with any grease you're going to get some creep, and it will definitely collect dust over time, so I would use it as sparingly as possible.
I used to do a lot of cycling in crazy weather. Where I went to college the temperatures (that I would brave cycling) would swing from about -20F/-29C to 90F/32C, and it certainly plays hell with lubricants. The three that I came to trust the most were a white lith (well-loved by the railroad engineers), some variation of Redline CV2 synthetic grease, and Teflon-based chain lube.
I did some Googling and it looks like average grease loses about half its oil content every four years, and that rate may double for every 10C increase. Given that if I'm going to crack open a camera, *I* probably only want to do it once during its lifetime. It probably came with some variation of either petroleum grease, petroleum jelly, or something like sewing machine oil, with maybe a 40 year lifespan. Not bad, considering the builder may have been speculating as much as I am (and probably wasn't expecting someone to still be using the camera 40 years later).
If I had to gamble on someone else's camera, I would probably go with a red synthetic grease. If I were working on my own camera, I would probably use a white lith and fret about the dust accumulation (and crack the camera open again in five years to check), or use a microscopic amount of Teflon-based oil, cross my fingers, and forget it. The less expensive the camera, the more I would probably lean towards the oil.
I have a toy camera that looks like it was lubed with petroleum jelly at the factory, and it's maybe 20 years old at the most, and it's having lubrication issues. For a camera that costs pocket change, another dab of petroleum jelly seems like the logical choice, but I suspect if I had some kind of gentle Teflon spray it might outlive the rest of my cameras. Assuming I didn't sit on it. 

Conversely, my Great Wall is having lubrication issues, too, and I have no idea what I'm going to do there. It seems like there's so much potential for weep and creep in that thing that it makes me nervous, but I thought of using that to my advantage. A drop of oil in the cable release hole would probably fix nearly anything on the shutter side. 
