I would like to switch banks and need your opinions

I have TD bank debit card that I use as my main card and the card will expire soon. My mom told me that I should apply for a credit card so I can build my credit history. So I was thinking of switching bank to Bank of America since my parents have an account there and they said that its a good bank.

Since my TD bank debit card will expired I might as well switch and open up new debit and credit card on Bank of America.

My question is that. Do I have to withdraw all the money I have on my TD bank debit card before I close it or can I transfer the money to my new card? but will there be a fee?