"Because of my father's influence, I started playing the guitar."
"I picked up the guitar because of my father."
"My father got me into playing the guitar."
"influence" 「影響」
"picked up" - "to pick up" 今回は「拾う」という意味ではなく、「始める」という意味を表します。
"I started playing the guitar." と "I picked up the guitar." は同じ意味です。
"my father got me into ◯◯." 「父の影響で〇〇を始めた。」