In the future, I plan to learn to play several more instruments and hopefully become a member of the band.
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'Hopefully' is being used as a parenthetical expression to interrupt a thought and not as a conjunctive adverb joining two sentences.
Since it is functioning as a parenthetical expression, you need to punctuate it with two commas.
"...and, hopefully, become a member of the band."
Your bare infinitive "become" is dangling in the air. One does not know where your bare infinitive belongs to - the reader has the choice of two verbs plan and learn and you make the reader try to find out how you constructed this sentence.
That is no good. I would choose the simplest and clearest formulation: ... and I hope to become a member of the band.