Never leave you coins on an exchange, Binance is an exchange. To have full control over your asset, use noncustodial wallet. Cold wallets are safest wallet type.
That is also my concern as OP is clearly trusting an exchange that will never be reliable at all times. So as early as now OP, move it to your own non-custodial wallet so that your privacy and security will be more possible. However, I am happy that you are now starting to live your dream. I just hope that you are doing DYOR first and gain sufficient knowledge in bitcoin investment before your start taking the risk of investing in bitcoin.