A number of commentators have objected to importantly as a sentence modifier (sense 2) and have recommended important instead. Actually both the adverb and the adjective are in reputable standard use in this function. Important is always used with more or most<had bronze weapons and composite bows; more important, they utilized the horse and war chariot — Harry A. Gailey, Jr.><second and most important, the book contains no important woman character — F. Scott Fitzgerald>. Importantly is somewhat more flexible in not requiring more or most<sticks and, just as importantly, unsticks easily — Phoebe Hawkins><importantly, the leaven in the mixture is quality — George O'Brien>.
Examples of IMPORTANT
Diet and exercise are important for health.
In his editorial, he made several important points.
Scientists have made an important discovery.
Doing her job well is important to her.
He's one of the most important scholars in his field.
Origin of IMPORTANT
Middle English importante, from Medieval Latin important-, importans, present participle of importare to signify — more at import