If you choose an online savings account from an institution with FDIC insurance, then your funds will be protected, even if the online bank were to go out of business.
Like other savings accounts, withdrawals from high-yield savings accounts may be limited to six per month, and going over the withdrawal limit may trigger a fee.
Money market accounts can be found at both traditional and online-only banks and are similar to traditional savings accounts in terms of liquidity, safety, and transaction limits.