You'll be able to get into a public school that you are in the catchment area for, I presume that you have to provide something like your address. I think you will be guaranteed entry as (in highschools) there are nearly always extra spaces- and if you are in the catchment area for it then I'm pretty sure they have to let you in.
You can also apply to schools outside the catchment area, if you think they are a better choice for you, or if your parents work near there etc. They will probably still let you in, it isn't like in England where primary school classes all go to different high schools (most- there are exceptions- people in your primary class will go to the same highschool)
I don't know anything about private schools, so couldn't help you on that.
Also you can go to catholic schools which are good if you are religious as they are more likely to be accommodating to any religious belief you may hold (other schools have to this as well but just usually religious schools have like more private space for any faith, eg Islam). Again not sure how common this is, but in my town there are 3 highschools (capacities of about 1,800) and 1 of them is a catholic one so there should probably be nearby to where you are moving.
Any questions about schooling just ask, hope this clears things up! And if you need specific help with schools or whatever, the local council of where you are moving too should be able to help.