I just wanted to add my two cents, for what it's worth: acrylics work best - I've tried oils, they do not work on vinyl, imo. Depending out what you plan to do with with the finished figure, applying a sealant is not always necessary. Once the acrylics dry they tend to be about as resilient to abuse as the original paintjobs. They will crack and peel, though, if the figure is actually played with. They also can be "washed" off/peeled off if they are exposed to too much moisture. I've had problems getting sealants to dry. They can remain sticky (some for years) and really ruin a nicely painted figure.
Also, when possible, use the fewest number of layers as possible. For a total overhaul of the paintjob, you will need to start with the base color. Skip primer other than base color. My experience using primer on animal figures is that they do not need it. As A-J described, drybrushing (dipping the paintbrush in the paint then "painting" a piece of paper or towel until very little paint remains on the brush) is very effective for highlighting and shading. Practice on a piece of paper first if you're not entirely comfortable with drybrushing. Less is best when applying paint, as you can always apply more to achieve a desired look, but once it is on, it's much harder to correct. So get comfortable with drybrushing before attempting it unless you have figures to practice on. It is exactly what it sounds like - painting with a dry brush.
Also, apply light colors first, then add dark. If you try to use white or yellow to cover black spots, you will see why.