(3) is best. But it's more natural to have this word order:
荷物が三つあります
(1) is grammatically incorrect. "持ちます" (mochimasu) means "to hold" or "to carry," but it's not used in this way to express possession.
(2) is a very formal way to say "to have" or "to possess," but it's not used in everyday conversation and doesn't fit this context.