Hi there,
I've been in Korea almost 4 years now. I don't have time to write a huge response, but I'll see what I can do . . .
First off, I don't know of anyone who has gone through Teach Away. I personally went through Footprints, and I know quite a few people who went through Ask Now. Of course, you are bound to find complainers everywhere, including those who complain about FP and AN, but my experience is that these are two of the best recruiters. I haven't heard of many problems.
You didn't mention about your qualifications or when you plan to come to Korea, but I always recommend that people try for public school jobs. There are some good hagwon (academy) jobs, but they are few and far between. If you want to try for a public school job, you should apply this fall for the spring semester (in Korea the school year begins in March). Also, Seoul is great, but you'll have much better luck if you are willing to work outside of Seoul. Try the EPIK program or for example, the DMOE (Daegu). I've lived in the countryside for nearly 2 years now and it's not so bad. The people are great, the air is cleaner, and you're never further than a 2 hour bus ride to a major city.
Anyway, you are hardly the first or the last person to have a million questions before coming to Korea. My advice is just to get connected with one of those recruiters, apply for public school jobs, and head on over.
Korea is a surprisingly easy place to transition to. I don't think I've ever met anyone who has regretted coming to Korea. I do know a few who were seriously ready to leave after a year. But then there's people like me who just keep staying year after year after year . . .
Good luck!