There are dozens of Flying Schools out in GA land prepared to take your money and give you a G3 Instructor rating.
Sure you need to ask around to pick a good one but more importantly you need to get work with that rating when you have acquired it.
The question you should be asking is can the school that you get your rating with give you work, enough work to warrent getting the rating with them, or is it a case of 'Next please' to be on the next course and instantly forget the guy who has just finished the last course.
IMHO there are more unemployed Grade 3 Flying Instructors in the system than there are potential jobs, and even those jobs that are around do not have sufficient work to justify an instructor working for that school.
Remember, you do not have a paid salaried position as a flying instructor, you are just a casual instructor there to be paid for any training that you do. You can be hanging around for a long time to get even some casual work.