See this question for some caveats. There is nothing positively wrong which is reported about it, but it seems to use custom format and password-to-key processing, which means that it was not well analyzed. I see no mention of an integrity protection. Therefore I would recommend caution until further analysis.
Assuming that AESCrypt does everything right (including integrity checks), then yes, sending by email files which are protected by a password is fine... provided that you choose strong enough passwords, and that you have a way to convey the password to the intended recipient with all the needed confidentiality. It would not buy you much to use both the innate encryption features of RAR and an additional encryption layer, especially if both use the same password.
Systems which support asymmetric encryption like GnuPG will still make your life easier. You still have to make sure that you have the right public key (the one owned by the recipient), but at least it is a public key so you can transmit it securely with less constraints (you can dictate the hash by phone, but you do not have to fear people who merely spy on the phone line, contrary to speaking a password over the phone).