Yes, all homeownersl do pay school taxes, ad valorum property taxes, and possibly other types of taxes.
The above link should take you to a pdf file giving you information about different taxing entities for the 4 counties in and around Austin. To know exactly which entities have the right to tax, you will want to have a specific address.
If you have specific areas in mind, it will be easier to give you an idea of what the property taxes are, based on 2008 assessed values and tax rate. Our actual tax bills will not go out until after September.
If you are at or near 65 YO, you will be entitled to an Over-65 exemption which will ensure that the taxes for the school distrcit attached to your homestead will not increase. This is also available as a Disabled exemption even if the person is younger than 65.
Please feel free to contact me if you would like more information specific to your needs.
Best wishes and welcome to Austin!