Don't get too excited about CELTA. Any TEFL certification will do usually. But get at least the 60 hour variety. As far as your non-native concern as long as you speak clearly with proper pronunciation and you can be understood it's fine. Native speakers are preferred but there's a serious shortage of teachers right now so the emphasis is on speaking clearly. Please refer to a post regarding the documents you need for job seeking. Search "the five things only" on this site and read it well. Also whoever starts emailing you do your DUE DILIGENCE. Use search engines to gather information on the recruiter or school to avoid getting hurt or in a bad school. Peace.