Hopefully, actually, basically, amazingly, fundamentally, surprisingly, significantly, essentially—these are all common ways to begin a sentence, and you can throw them out. My favorite story about “actually” is from a friend whose young granddaughter started many sentences with that word. Her grandmother asked her what “actually” meant, and Nicole thought about it and finally answered, “Actually, I don’t know.”
Adverbs can be redundant. There is no need for a band to blare loudly. Is there any other way to blare? Do you clench your teeth tightly? Laugh happily? Weep sadly? Are you totally amazed? Can you be partially amazed? Isn’t that like being partially pregnant?
When you use an adverb, determine whether it is doing any work. Does it contribute to the meaning of your sentence? If not, cut it out. It’s deadwood.