An initialization vector never needs to be secret. If it needed to be secret then it would be called a "key" instead of a "vector".
Generally, the initialization vector requirements are only dependent on the mode of operation, not the choice of the block cipher. The parameters of the mode of operation, such as the IV size, may however depend on the block size of the used block cipher. For CBC mode the IV is always the same size as the block size, which is 16 bytes for AES.
For CBC mode, you can use a fixed initialization vector when the same key is only ever used for one message. Note that this also means that you should not reuse the IV for multiple versions of the same message. If your key is calculated deterministically from the login credentials of the user using a hash, this will not work. You may however use a changing salt and a password hash such as PBKDF2 or Argon2. The unique salt and therefore unique key then take the security role of the initialization vector.
A changing but predictable initialization vector is bad when the attacker can choose a message to be encrypted and then observe the ciphertext. It would be possible to observe if a IV / plaintext combination would result in identical input to the block cipher, resulting in identical ciphertext. So using a predictable IV could leak information about previous plaintext having a specific value. An attacker-chosen initialization vector is equally bad, of course, even if she can't choose the message.
A cryptographically secure (pseudo-) random initialization vector - stored next to the ciphertext - is generally safe for all modes of operations.
Please note that you'll often also want to calculate a MAC over the data, to make sure it cannot changed without detection. If you don't do this then an attacker can modify the ciphertext and observe the reaction when you try to decrypt. This may allow an attacker to perform padding or other plaintext oracle attacks and retrieve the plaintext. If you stored the IV next to the ciphertext then you should also include the IV in the calculation of the MAC.