GPA only wraps GnuPG itself, thus all operations are (somehow) possible using the bare gpg command line application.
I guess you're not after sign and compress, but sign and encrypt. Compression is added automatically before encrypting clear text messages. Compression could be enforced by adding an --compression-algorithm zip parameter (the only algorithm that must be understood by all OpenPGP implementations).
Regarding sign and encrypt, you will have to define the recipient and use both the --encrypt and --sign commands, or their respective short forms -e and -s. In the end, all you missed is the recipient:
gpg --recipient [uid/key-id] --sign --encrypt
For automating the encryption and passing a passphrase, you already found the required options. -a or --ascii adds ascii armoring, which usually is not required but might prevent some transmission issues sometimes, but enlarges the file a little bit.