Ellipsis (plural ellipses) deserve some discussion. Check out the following sources:
In prose, ellipses are not generally needed at the beginning or end of a quote. The rule is different for poetry – and if there is confusion between the above sources – my rule is no ellipsis at the beginning or end of a quote. Even if you end a quote before the period. Even if the first part of the sentence is left off.
MLA has gone back and forth on whether brackets […] are needed to clarify that you inserted ellipsis rather than include punctuation found in the original source – so that one is you call. Just be consistent.