Plus Spell or Elemental damage

Using a Frostbolt self cast build, is it better to have +Spell or + Elemental damage items?

Also, when it says "add # to # to cold attacks, does that mean all attacks? Spells and melee or does it have to say "to spells" to affect Frostbolt?

When items have "add # to # to attacks" it means attacks only, it will not add those to spells. There are other items that can add damage to spells. Items like the added cold damage gem apply to both, because it doesn't specify one or the other.

For Frostbolt specifically, it will be increased by spell, elemental, cold, and projectile modifiers. You can use any of these to increase your damage.