The rule, if one is to accept rules as absolute, is to avoid beginning sentences with conjunctions.
This is the recommendation of Warriner and Lunsford, two reliable authorities used in US classrooms.
Like most rules, it is sometimes broken by artists and professionals who know what they are doing. Beginning with a conjunction can add rhetorical weight to the sentence, particularly if the preceding thought is well and succinctly developed.
When my students (US native-speaking, university-bound adolescents) try this, they often achieve a horribly childish polysyndeton effect, and are generally roasted over a slow fire by their instructor.
If one is certain enough in one's convictions to stand up to a fiendish teacher or an unforgiving editor, one may try it. But do so at your own risk.