My experience is in China; I've known a number of Korea veterans and I gather that many things are similar there.

You've opened a big, big topic and it's really impossible to deal with all of the aspects at once.

In either country, it's important to try and guard yourself against being ripped off. It happens here every day. You have to be very, very careful dealing with schools in this part of the world.

First of all, if the ads don't name a school, odds are that they are from recruiters and in that case you don't want to pursue them. The litany of abuse by recruiters in both countries goes on forever. Recruiters often represent schools that can't fill their teaching slots on their own, often because they are in terrible cities and/or pay crappy salaries and/or have a bad history of teacher treatment. It's a SELLER'S MARKET for English teachers here; there are zillions of unfilled jobs to be had here. You don't need a recruiter. Go on the internet and find the jobs listed in a thousand places. If they don't name a school and don't give you a contact directly at the school, forget it and go on to the next ad. If you're not sure, ask them if they are an employee of the school in question. You might still get ripped off going direct, but the chances of this are a bit lower than they will be working with a recruiter.

Beware of bait-and-switch tactics, especially if you're coming in from outside China or Korea. Baiting-and-swithing is a beloved tactic of recruiters! There are many cases where people have been lured here with glowing ads full of promises, only to find themselves being coerced to sign a contract for something very, very different. Even if you have a contract full of wonderful stuff, you might have a hard time getting them to live up to the contract. Contracts are merely suggestions in this part of the world. Of course, don't sign anything that doesn't give you what you were promised. If a contract isn't honored, make noise and give them a reasonable time to fix things. If it doesn't happen, STOP TEACHING until the promises are fulfilled. Be prepared to leave town if you have to...there's a lot of other jobs to be had and some will be much better.

Another place to beware is things that you get at the end of your contract...bonuses, airfares, and so on. Many school owners have made an art form out of finding ways to not pay these, including such tactics as firing you for "poor performance" a week before your contract ends. Try to negotiate earlier payment of these items, and try to avoid having too much at stake on the end of the contract. The school is indeed entitled to some means of ensuring that you will honor your contract in full, but then so are you.

Mos schools will indeed honor such terms as an apartment (try to get a FULLY PRIVATE apartment; many are shared!), a Z Visa/Residence Permit (EXTREMELY important!), travel allownaces, and so on. NEVER take a full-time contract that doesn't include a residence permit and either an apartment, an adequate housing allowance, or a salary high enough to let you rent your own. If possible, inspect provided housing before you sign anything. Renting an apartment in China is quite a story in itself but should be told in another thread.

There's so much to talk about with respect to job ads and contracts. This is only the tip of the iceberg.

Not being a 20-something should not be a problem for you. Being gay could be. It still has a high stigma here and could cost you your job if the school finds out. It's truly a case-by-case situation...some schools (indeed, some whole towns) will totally freak out at the slightest hint that you might be gay, others will be more tolerant as long as you do good work and are discreet. It would probably help you if you are careful to not involve students or Chinese co-workers at the school where you are employed...there are NO secrets in this country. It will probably help you if you stick to larger, more progressive towns rather than going into the sticks. Shanghai and Suzhou are reportedly among the more gay-friendly places in China. China does have a gay community, both foreign and domestic, and my gay friends here have eventually found ways to connect to it.
The advice of this old flaming heterosexual is that no matter where you go, you play these cards very, very close to your chest indeed.

There's great info at this site and I am a regular here myself. If I may be so bold, you can also find a lot of information about living and working in China on my forum, Raoul's China Expat Saloon. You can take a look at our public side at http://chinateachers.proboards17.com/index.cgi You will find a lot more info there than I could ever load into one post or one thread.