Choose a synthetic brush for latex (water-based) paints. Typically these are polyester, nylon or a blend of the two. For oil-based paint always use a natural hair paint brush, or a blend of bristle or ox hair with synthetic. Don't use a natural brush with latex; you'll only end up ruining an expensive brush.

I would add that you can indeed use a blended poly brush for oil paint… use pure bristle only when you absolutely need a fine finish like when varnishing furniture or woodwork… Nylon will not work however with oil paint…