I am not sure why would you use Coinbase as a wallet.
Exactly. I can't understand why it is so difficult to distinguish between an exchange and a wallet.
Coinbase is an exchange (website), not a wallet.
Electrum is a wallet (computer program), not an exchange.
See, really easy to distinguish.
People stop storing your coins in an exchange. Store them locally, on your computer in a wallet.
What is the best crypto wallet with the lowest fees and fastest transaction time?
A good wallet will set reasonable fees so that your transaction is received in a reasonable period of time. But in the end, you are free to set the fees manually.
The transaction times will depend on the fees. If you set them too low, the transaction time will increase.The reason is that miners prefer to include transactions with higher fees in the blocks they mine.