What information should I send along with an AES ciphertext and is there any standard to do that?
What you are looking for is a definition of PEM, privacy enhanced mail. Obviously PEM is not just used for mail anymore. The definition of the header lines seems to be best described by section 4.6: "Summary of Encapsulated Header Fields" of RFC 1421: "Privacy Enhancement for Internet Electronic Mail: Part I: Message Encryption and Authentication Procedures". Obviously for PGP specific header fields you'll have to take a look at the OpenPGP format, specifically the section about ASCII armor.


  Then, i would like to use a comment like the one showed above to store my ciphered messages as plaintext. Assuming i want to do that for a message ciphered using AES, which informations should i store ?


That depends on the scheme you've chosen. For transport security the minimum would be the IV, the ciphertext and an authentication tag over both.


  Should i store the AES mode used for encryption ?


That depends. You could store a protocol version instead which determines which mode is used. You should not just store the mode without authentication and then proceed to process the message based on the header fields. That would give an attacker to decide which operation is performed on the receiving side. You need to keep control over what is performed on the receiving side.


  Should i store the AES implementation i used ?


No, the implementation of the block cipher should be irrelevant if you've decided upon a well defined protocol.

You could store a version of the software implementation of a protocol. In that case you may be able to work around possible bugs within the implementation. I've seen quite a few instances where the implementation of PGP did matter.


  Should i store the initialization vector ?


Yes, unless you've got ways of establishing the IV out-of-band (e.g. an operation over a message counter included in a message counter, or a counter kept in sync at both sides). If unsure include a random IV of sufficient size.


  Should i try to be compliant to some standards while storing these informations ? 


It's strongly advisable to keep to well known container formats such as CMS or the already named OpenPGP yes.