Hm, how long are you planning to stay in Korea? If you're planning on just staying for a few weeks, then a hostel or a hotel would probably suit your needs best. It's difficult to calculate rent and utilities for a week since it's done on a monthly basis like in most countries.
If you're thinking long term, the cheapest option is a goshiwon (고시원), which is basically a closet and will cost you in Seoul about 200,000 won a month without having to put down key money (보증금).
The more popular option would be wolse (월세), which is usually done for one-rooms (원룸), officetels (오피스텔), and villas (빌라), and it involves a regular monthly payment in addition to putting down key money. For a decent place, you can expect to pay about 600,000 won a month. Key money is another issue. That can range from 3,000,000 won to 20,000,000 won depending on the size and location of the home. Key money is crazy expensive in Seoul--that's why most Koreans in Seoul live at home with their parents, saving up so that they can afford to move out when they marry.
The last option, and the most expensive, is jeonse (전세), and with this option there is no monthly rent. The downside is that the key money is RIDICULOOOOUUUUSSSSS, usually from around 20,000,000 won to upwards of 100,000,000 won. With the 전세 system, you're actually giving the landlord kind of a loan---they take your money and invest it somewhere else, but you get your money back in full once your lease is up. I have no idea why anyone would want to take this housing option, but I've been told that it saves money in the long run since you're not paying a monthly rent. (Also, the only option that allows you to rent on a monthly basis is a goshiwon. The other two are usually year by year leases.)
As for utilities: my electric bill is higher in the summer because of my air conditioner---the highest that has been was about 10,000 won. Gas is definitely more expensive. For me, during the warmer months, it can be as low as 900 won. During the colder months, when I pump up my floor heating and roll around in the warmth, my gas bill has been around 200,000 won. Some buildings also have additional fees, like if you have a security guard, you'd pay a security fee, or some others I know pay a month fee for their elevator.
All of that applies to Seoul where I live. I think other cities might be cheaper. The country side is definitely the cheapest, but it's kind of dull.