You should do some more research online on this.
With public health, you DEFINITELY want to get a masters at bare minimum. Some people consider a masters the new bachelors. There are already tons of masters out in public health, but with a masters you can do quite a few things (state health agencies, CDC, NGOs, think tanks). If you can get a masters degree from a top notch public health school (Harvard, Hopkins), it will improve your career prospects in public health. It's also important to note that public health is sometimes less the degree you have compared to the people you know and the connections you make. It doesn't matter if you have a bachelors and some other person has a masters if you know the employer and the masters guy doesn't. The employer will hire you. For job prospects, you need to start networking like crazy and making connections (it's not who you know, but who the people you know know).
With a PhD, you can either work in academia, or also with work with the same agencies I mentioned before. Having a PhD increases your job prospects more, though you have to be careful because sometimes a PhD might make you too competitive for a job you want and then an employer may not hire you because they don't want to pay you so much more for your PhD degree.
Think through it carefully. Definitely get a masters degree since it's essential to work in public health as well as a necessary stepping stone to get a PhD. Get a PhD if you want to go into academia and pursue a career in research, but don't expect to get a tenure position as those are very competitive and not everyone can get them. Good luck!