I agree that the Schafer end probably has the most bang for your buck. A good trip would be out to Lathrop canyon and down to the river, and then back. Lathrop is a fun drive, and doable in a stock 4runner.
The only narrow shelf roads are at Murphy Hogback and HardScrabble Hill. Murphy is at about the half-way point, so you might as well drive the whole thing if you go that far. The overlook at White Crack (just on the Schafer side of Murphy) is worth seeing, but again is a good long drive from the start of the road.
Whether or not the road is driveable in one day depends on how hard you want to be on your body and on your truck. The road out to Musselman is pretty smooth, but past there it gets rougher, with a lot of water channels at 90 degrees across the road. They're not deep, no chance of bottoming out, but they will jar you and your suspension a lot. If you're OK with hitting that kind of thing at 20mph, a one day trip is very feasible. If you're a cautious wimp like me, taking 2-3 days for the whole route is much more pleasant. Plus I like to stop and hike.
[MENTION=10182]smallfry[/MENTION] is correct in that the trafffic is light, and won't really affect your trip much.
I think I used 18 gallons of gas on the trip, but that included a tour through Gemini Bridges and Bull Canyon on our way to the Schafer switchbacks. The only reason to take extra gas would be if Upheaval Wash was flooded when you got there, requiring backtracking all the way back out. Not likely at this time of year.
