With private schools you may have a greater chance of being hired for an opening fresh from graduation. Less people tend to go for these positions because they have lower salaries and you may have less protection with your position. From first hand experience I have seen the trials that come along with the lower salary for full time teachers and lack of job protection. However, many teachers may prefer the environment, educational practices, and ethics of private schools. There are many private schools that are wonderful to work in.
In public schools you tend to have a higher salary and after a few years, if you make it a few years, will have job protection. You have a great deal of benefits but have to deal with a lot of pressure from the state and administration for student performance and standardized tests. Generally public school positions are the most desirable because of the higher salary and benefits of being 'mainstream.' If you are fine with the classroom politics and testing/evaluation pressure then you will definitely benefit from the higher salary.
It's quite a choice. Do your beliefs match more with a private or public school, and would you sacrifice the higher pay of the public to work in the private? If you do choose to work in the public school system the question then becomes how do you worm your way in?
The main way is to substitute teach. It is pretty easy to get hired, but is a thankless job that is unreliable at best. You can get called at 5:30 a.m. to teach that day at 8:30 or get a call at 5:30 a.m. saying your job for that day was cancelled. Not to mention that if you don't accept a posting within it's first few minutes it will be gone before you have the chance to blink. It is also nearly impossible to survive on just a substitute teaching salary. You need to be a long-term sub, manage to sub every day, or have another job to make ends meet. Furthermore, as an education student you always hear horror stories: having no plans, students that are uncontrollable, having no organization or information on your schedule. It seems altogether an undesirable job.
Subbing has worked for me this year because I have also managed to get a part-time job as the director of one of the after school programs run by the local YMCA. It's about three and a half hours a day and leaves my mornings open to sub. I have been hired as a substitute in three districts and sub about two mornings a week (or more) on average.
If you want to be in the public school and are not one of the lucky few to be hired directly out of graduation I highly recommend subbing. Especially if you have some kind of back-up salary or other kind of income to support you. Subbing lets you get your name out into the schools while giving you hands-on experience. It may not pay much money but you reap the benefits of the experience. (If you do go the subbing route do get Jobulator. Its $40 for a whole year, works directly with the subbing system most schools use (AESOP), and can be downloaded to your computer and smart phone. If you set it to update every minute it will tell you automatically if a new subbing position is open. I have gotten many of my days thanks to this app!)
