How much should I save from each paycheck for taxes if im a 1099 contractor and will be a dependent on my parents tax return?

I am starting a new job as a 1099 contractor. From the research that I have done, it looks like you are advised to set aside 25-30% from each paycheck for taxes. I am wondering if this will be any different because my parents will file me as a dependent on their tax return. This is in preparation for next years tax return.

My old job was a standard W-2 employee so my taxes were withheld.