Question one can have many answers - depending on who you ask.
1. Necessary qualities:
1. honesty 2. commitment 3. flexibility 3. creativity 4. sense of balance 5. democratic - not the party but the attitude of listening to all sides before making decisions 6. respectful 7. consistent 8. realistic 9. being teachable 10. Acknowledges and applies standards of teaching and ethics
There are many more necessary qualities and you can read resources from other websites:
Sufi Amanesis: Qualities of a Teacher
ASCD Blog: ASCD Poll: Qualities of Teacher Leaders
2. pros and cons of public vs private schools:
Adventures in Parenting: Private vs. Public school - weighing the pros and cons
Berkeley Parents Network: Private School vs. Public School
pros and cons of public vs private school - Google Search
3. average pay of new teacher in NY?
According to the NEA, the average starting salary for a teacher in NY is $42,512.00. The average teacher makes a little over $59,000.00. Teachers are contracted employees so the raises may be up to the school board. Just an aside, in New Jersey, first time teachers are going to be receiving $50,000.00 in some districts.
NEA: Professional Pay - News
4. Your major to be an effective teacher?
What grades do you want to teach? Pre-school, grade school, middle school, high school, college? Do you want to go into Special Education? You need to pick some area - you cannot get credentialed for all of them at the same time. You pick what you like - picking a major just to make you marketable does not play out well. You may come to resent your choice. A Bachelor's degree will get you started in teaching. You can decide from there if you want to pursue a Master's or even a Ph. D. I have known many teachers who have gone back to college to get a degree in Administration, so they can move into administrative positions in the school system.
5. Transitions:
It is not difficult to transition from grade school to middle school or to high school but you will need additional schooling and certification. There is financial assistance out there but you may not be eligible for grants, since you will already have a degree. BUT there are organizations out there and resources for teachers who want to go back to upgrade their teaching and advance careers. There are times the school or the school district will aid the teacher. I worked for a private school that sent a teacher's aid back to college to get her special ed degree - she was two years short. They paid for it all! The only thing she had to do was sign an agreement to work for them for five years. What is five years? Not much in the scheme of things.
Also consider applying for a Fellowship:
NYCTF - FAQ - FAQ
Sorry this is so long. How much have you read through NEA or other teacher organizations?
NEA: National Education Association
Educational Associations