What characteristics would make an encryption absolutely unbreakable? what characteristics would make an encryption impractical to break?

There's no such things as an unbreakable encryption. If an encryption is devised, it will eventually be broken/decrypted. However, there are certain measures or characteristics that can be put in place to prolong decryption like using a one-time pad encryption. This means the key is used only once; using a key once is a pretty good idea since a strong algorithm will be of no use when the key becomes known. This characteristics ensures that a new key is required for decryption on successive attempt. You could also consider adding a long sequence of characters or adding an extra layer of security by upgrading to 256 or 512 bit encryption, also use salting and multiple algorithms.