The rest of the calculations were done but I wasn't sure if they were right because I've never tried this before and thought I'd ask those that know more than I do. The app note I linked had a filter cap configuration for dealing with inrush current and while I was doing research on the calculations for that I stumbled on this circuit and because it seemed simpler I was curious if it would work.
The process goes like this:
1. Draw a PFET on your piece of paper. Make sure the body diode is pointing against the normal flow of current.
2. (Optional) add a zener from G to S, to prevent Vgs from getting too high.
3. We want the MOSFET to stay switched off initially; capacitors tend to hold voltage steady. Since the capacitor will be discharged initially, it'll have zero volts across it. We want the FET to be off initially, Vgs = 0 volts. Therefore, we should connect the capacitor from G to S (in parallel with the optional zener).
4. We need the FET to eventually turn on. A PFET is turned on by a negative Vgs, S is fixed at the positive supply, so this is great because we just have to pull the gate to ground to turn it on (if you used an NFET, this is where you would get stuck). Therefore, we connect a resistor from the gate down to ground.
Design done, with simple reasoning only. Now, the only issue is that the FET might turn on sort of gradually, and might burn a lot of power while it's only partially turned on. If you want to avoid that, you'll need some more active components.
Oh, I also want to say liquibyte. NEVER use Google images for circuits. I did that once, and screwed up an order of circuit boards. The picture I was going off of, had the source and drain switched. Really messed up the entire circuit. However, if I had gone to the link where the picture was, and read the thread, I would have known it was wrong, as it was mentioned in the thread. Lesson learned.
I think surely the lesson here is, understand and test your circuits rather than blindly accepting schematics from ANY source. If you got circuit boards fabricated without ever testing or thinking "What's the VGS on this FET here?", then you're orders of magnitude short of due diligence. Google images is just fine (wonderful, even), as a source of inspiration.