I generally work on stuff that isn't in the 3 3/4 scale, but if you want an idea of how to prevent any problems:
1 - Wash the figures with Windex or something that can breakdown grease (aka the mold release agents)
2 - Prime it. I'd suggest using what Doc said or any spray paint you find in the home-improvement area of a store. You want something that ISN'T acrylic and something that goes on smoothly and can be buffed/sanded if need be. Also, these "hot" primers tend to need about 24 to 48 hours to completely cure. So let it sit for awhile before you sand or add paint.
3 - Paint it. For this, I'm with just about everyone else who does figure painting...use acrylics. This is why a primer is important. Most acrylics will lift off if they don't have anything to "bite" onto, and bare plastic doesn't give them much. So if you plan on re-posing your figures or handling them often, then a primer is a good way to ensure the paint will stay on. On top of that, you can a clear coat (Krylon has some nice ones, or you can try Future), which will make it even harder for the paint to lift off when you're handling it.
I have several pages on my website below that go into more detail, but may not apply to what you're doing. But if you want more information, feel free to check it out or ask away here. Trust me when I saw we've all been there.