For transporting messages you need a transport protocol, not just a block cipher mode of operation. The handshake of a transport protocol is used to authenticate the entities and to establish session keys (and more). Those are essential activities to protect the messages send using the protocol. TLS is most common, where DTLS is explicitly specified for UDP - i.e. separate packets.
Blocks have a specific meaning in cryptography; they are the input of a block cipher. So if you have chunks of 256 bytes then you need a block cipher mode of operation for the messaging part of your protocol. In that case an authenticated mode of operation such as AES-GCM is best. This requires the protocol to specify a unique nonce, and it will generate an authentication tag for the encrypted message.
As you've specified a specific packet size you may also look into modes that were explicitly created for packet based security such as AES-CCM.