In my thoughts, Binance and Coinbase both have the feature of creating a wallet. Believe it or not, I've already browsed and saw differences between Binance and Coinbase, interface-wise I love how Coinbase looks because of its visual appearance.
So my question is, based on user experience, where is the safest and stablest wallet I can use so that my BTC won't magically disappear like what have happened historically.
Thanks for reading my really newbie question and soon I'll write about how this specific player who got me into bitcoin helped my private game server grow (its an old game, but runescape is still older)
Binance certainly does not have the feature of creating a wallet.
Unless you use your exchange balances as a hot wallet, which is completely stupid in my opinion. If you look at what happened in the past with people blindly trusting exchanges as a wallet, I think that you will agree with me as well.
Coinbase is not that much better. Even though they specialize as a "wallet provider", they still do not allow you control over your private keys. They even removed the option of signing messages with your previous addresses, which further takes away your control.
I strongly recommend, as others have stated, investing in a hardware wallet.