Personally, I find that doing the Rocco style is easier with flats, because their stiffness gives some resistance. Plus, they have a certain "old-school vibe" (jeez, I hate cliches) which suits that style.
On the other hand, the Jaco thing generally cries out for roundwounds (and he himself insisted on roundwounds "for that
funky sound"). Slapping sounds good, but different, on both flats and roundwounds (Larry Graham vs. Marcus Miller).
Since you've apparently got only one bass to cover all this ground, I'd recommend roundwounds... maybe something fairly stiff, such as D'Addario XLs.
You'll get lots of other recommendations, probably all good. In reality, funkiness comes from the soul and fingers more than from a particular type or brand of string.
Off my soapbox now....
