i don't use avg but i guess the answer is similar for all virus programs. to heal means avg made a backup of the file before it got infected and it will try and replace the infected one with the backup. delete just deletes the file completely. ok if its an attachment but not good if its a system file. remove to vault means it doesn't delete the file it saves it where it can't harm your pc. i would try to heal then move to vault, then as the last resort delete it.
heal: tries to remove the virus from file (doesn't always work)
delete: well... the file is gone
remove to vault: puts infected files into a quarantined(not accessible) folder
Since AVG is famous for producing false positives, that is detecting a virus where there is none, I wouldn't recommend to allow AVG to delete "infected" files right away.
You can always try to let AVG attempt to heal the file, but I am not sure if AVG makes a backup...
Moving the file to the vault is my favorite, since you don't lose the file and can easily retrieve it... and maybe scan it with another scanner to double check if you really got a virus and no false alarm!