Good advise eslguy.
I would add one thing. Reputable academies in South Korea sign with a company stamp in red ink.
The hiring officer of the school who stops at a handwritten signature has no intention of honoring the contract. (A fine example: Ahil English School).
Legally, handwritten signatures on employment contracts are worth nothing without that company stamp.
Having said that, I must add that, in some parts of Korea, with enough power or enough money, or enough juice cases, some authorities will accept anything.
ANET