OK, so from my info, there is no one type that has both of the traits you mentioned; the types that deal super effective damage to the most types have an unimpressive amount of resistances, and vice versa. I can however name which types are the best for each trait.
OK, so the type deals super effective damage to the most types is a tie between Fighting and Ground, with both dealing super effective damage to 5 types. Meanwhile, the type that has the most resistances is Steel by a longshot, with a whopping 10 resistances and one immunity.
Hope I could help!