Caulking a baseboard - which bit do you paint?
Personally I prefer to paint it the colour of the baseboard.  I tend to use Satinwood, and the thicker paint helps to mask the bead itself better.  It does require a steady hand as you really don't want to be accidentally painting that on to your wall (I hate masking tape).

As previous commenters have noted, the bead should not be all that thick.  When I install baseboard (or skirting board, as we call it in the UK), I try to use an adhesive like No More Nails as it saves filling or covering the nail holes.
If you are using nails then I would definitely suggest using a couple more to ensure you keep that gap as small as possible