Your employer will cover 50% of your health insurance. Keep in mind that dentists, hospital visits, medication or prescription drugs are very cheap in Korea. Your employer will also offer you a return flight to and from Korea. You will also receive a furnished apartment (shared or single depending on your preference). The great part of teaching in Korea- upon finishing your contact, you will receive a full bonus month salary. Work for 12 months and get paid for 13!
South Korea is safe and sanitary but I do recommend you get your Hepatitis A, B and C shots before leaving. It is also recommend you call the Tropical Disease center (get link) in case you plan on doing additional traveling during or after your contract ends. If you plan on traveling to tropical countries after your contract, you can easily get immunized in Korea.
For more information on available vaccinations, and who should consider them, you can visit this page: http://www.mdtravelhealth.com/destinations/asia/south_Korea.html
Yes, South Korea is a safe country with law abiding citizens. You may see demonstrations on the news or stories of concerns over North Korea. These stories are often over dramatized. South Korea has a large US army presence and is very safe for both men and women alike. I was there for 4 years and never had a problem. Research shows that incidents of violent crime are substantially lower in South Korea than they are in other Western countries, such as Canada and the U.S.
It is not recommended to break a contract because it looks bad and it may be difficult to get another job in Korea. If you have to leave for an emergency, employers can be flexible and arrange for you to leave and come back. If you want to terminate your contract, you must give your employer two months notice first so they can find a replacement. Your employer will then give you a release letter so you can leave. It is important to obtain a release letter because if you don't, you won't be able to work in Korea for 5 years.