What size of initialization vector (IV) is needed for AES encryption?
For both CBC mode and CFB mode, the initialization vector is the size of a block, which for AES is 16 bytes = 128 bits.  For CFB mode, the IV must never be reused for different messages under the same key; for CBC mode, the IV must never be reused for different messages under the same key, and must be unpredictable in advance by an attacker.  Using successive integers as the IV is fine for CFB but not fine for CBC.

Beware: The Wikipedia articles are currently (2017-08-11) full of archaic drivel about self-synchronizing ciphers and error propagation and other fortunately forgotten relics of the dark ages of crypto engineering from a bygone century.  I cite them only for the easily accessible statements of equations relating plaintext and ciphertext and their associated diagrams.

All that said, could I interest you in an authenticated encryption scheme instead, such as NaCl crypto_secretbox_xsalsa20poly1305?  Or, if you find yourself reaching for the letters ‘AES’ and ‘CBC’, you're probably lost in a vat of acronym soup and you may need help navigating crypto protocols more than you need help picking the right parameter sizes for a confusing crypto API that asks you to choose mode and then specify IV.