Although I bought my first Bitcoin through a P2P transaction with an exchange wallet, after receiving my first coins I have to resend them to an electrum Bitcoin wallet because it is safer.
Yeah, sending your Bitcoin into your own personal wallet is the best choice as those exchange's wallet isn't safe because they can have any rules anytime. Currently Bitcoin fees are still low and you can easily send those Bitcoin into your own personal wallet but you should be careful during creation of your personal wallet.
I would recommend you to completely format your drives and then install a fresh copy of either Linux that's the safest operating system or Windows which ever you prefer. Once it's fully install then download Electrum and install it and then create your wallet and save your seed phrase as well your private key. Once you successfully deposit your Bitcoin into your own personal wallet then you should disconnect the system where you install Electrum for best security.