I'd like to take a moment and agree with the FAQs page linked to you above. You sound a lot like the same position that I was in 6 years ago - a degree and a desire to travel - contemplating which of all these schools is best.
I found in my search I kept getting kicked over to the TEFL Worldwide Prague website. I researched for about a week, decided I'd never traveled to Prague before, so it was as good of a place as any, and I made the leap. That was over six years ago now and I've taught in the Czech Republic, South Korea, the UAE, and Germany since then. It's been an unbelievable ride.
And, yes, I needed that face-to-face course - it is my personal belief that all teachers need to be observed as they're learning their craft. In that list of countries above, I've seen great teachers (who always had some good training) and too many unhappy teachers (who cut corners in the preparation by either doing it online or thinking they didn't need it). What I found at the above school (I personally think it was one of the best moves I ever made!) was a really qualified staff and such practical teaching tips that I have felt confident every day that I made the right decision.
Best of luck to you as you start this journey and make your choice!